Statistical

Techniques

in Business

& Economics

Seventeenth Edition

LIND

MARCHAL

WATHEN

Statistical Techniques in

BUSINESS &

ECONOMICS

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Statistical Techniques in

BUSINESS &

ECONOMICS

SEVENTEENTH EDITION

DOUGLAS A. LIND

Coastal Carolina University and The University of Toledo

WILLIAM G. MARCHAL

The University of Toledo

SAMUEL A. WATHEN

Coastal Carolina University

STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS, SEVENTEENTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by

McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions

© 2015, 2012, and 2010. No part of this publication may be reproduced or distributed in any form or

by any means, or stored in a database or retrieval system, without the prior written consent of McGrawHill Education, including, but not limited to, in any network or other electronic storage or transmission,

or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside

the United States.

This book is printed on acid-free paper.

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All credits appearing on page or at the end of the book are considered to be an extension of the

copyright page.

Library of Congress Cataloging-in-Publication Data

Names: Lind, Douglas A., author. | Marchal, William G., author. | Wathen,

Samuel Adam. author.

Title: Statistical techniques in business & economics/Douglas A. Lind,

Coastal Carolina University and The University of Toledo, William G.

Marchal, The University of Toledo, Samuel A. Wathen, Coastal Carolina University.

Other titles: Statistical techniques in business and economics

Description: Seventeenth Edition. | Dubuque, IA : McGraw-Hill Education,

[2017] | Revised edition of the authors’ Statistical techniques in

business & economics, [2015]

Identifiers: LCCN 2016054310| ISBN 9781259666360 (alk. paper) | ISBN

1259666360 (alk. paper)

Subjects: LCSH: Social sciences—Statistical methods. |

Economics—Statistical methods. | Commercial statistics.

Classification: LCC HA29 .M268 2017 | DDC 519.5—dc23 LC record available at

https://lccn.loc.gov/2016054310

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a

website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill

Education does not guarantee the accuracy of the information presented at these sites.

mheducation.com/highered

D E D I CATI O N

To Jane, my wife and best friend, and our sons, their wives, and our

grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathryn

(Kennedy, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate).

Douglas A. Lind

To Oscar Sambath Marchal, Julian Irving Horowitz, Cecilia Marchal

Nicholson and Andrea.

William G. Marchal

To my wonderful family: Barb, Hannah, and Isaac.

Samuel A. Wathen

A

NOTE

FROM

THE

AUTHOR

S

Over the years, we received many compliments on this text and understand that it’s a

favorite among students. We accept that as the highest compliment and continue to

work very hard to maintain that status.

The objective of Statistical Techniques in Business and Economics is to provide

students majoring in management, marketing, finance, accounting, economics, and

other fields of business administration with an introductory survey of descriptive and inferential statistics. To illustrate the application of statistics, we use many examples and

exercises that focus on business applications, but also relate to the current world of the

college student. A previous course in statistics is not necessary, and the mathematical

requirement is first-year algebra.

In this text, we show beginning students every step needed to be successful in

a basic statistics course. This step-by-step approach enhances performance, accelerates preparedness, and significantly improves motivation. Understanding the

concepts, seeing and doing plenty of examples and exercises, and comprehending

the application of statistical methods in business and economics are the focus of

this book.

The first edition of this text was published in 1967. At that time, locating relevant

business data was difficult. That has changed! Today, locating data is not a problem.

The number of items you purchase at the grocery store is automatically recorded at

the checkout counter. Phone companies track the time of our calls, the length of calls,

and the identity of the person called. Credit card companies maintain information on

the number, time and date, and amount of our purchases. Medical devices automatically monitor our heart rate, blood pressure, and temperature from remote locations.

A large amount of business information is recorded and reported almost instantly.

CNN, USA Today, and MSNBC, for example, all have websites that track stock prices

in real time.

Today, the practice of data analytics is widely applied to “big data.” The practice

of data analytics requires skills and knowledge in several areas. Computer skills are

needed to process large volumes of information. Analytical skills are needed to

evaluate, summarize, organize, and analyze the information. Critical thinking skills

are needed to interpret and communicate the results of processing the

information.

Our text supports the development of basic data analytical skills. In this edition,

we added a new section at the end of each chapter called Data Analytics. As you

work through the text, this section provides the instructor and student with opportunities to apply statistical knowledge and statistical software to explore several business environments. Interpretation of the analytical results is an integral part of these

exercises.

A variety of statistical software is available to complement our text. Microsoft Excel

includes an add-in with many statistical analyses. Megastat is an add-in available for

Microsoft Excel. Minitab and JMP are stand-alone statistical software available to download for either PC or MAC computers. In our text, Microsoft Excel, Minitab, and Megastat

are used to illustrate statistical software analyses. When a software application is presented, the software commands for the application are available in Appendix C. We use

screen captures within the chapters, so the student becomes familiar with the nature of

the software output.

Because of the availability of computers and software, it is no longer necessary to

dwell on calculations. We have replaced many of the calculation examples with interpretative ones, to assist the student in understanding and interpreting the statistical results.

In addition, we place more emphasis on the conceptual nature of the statistical topics.

While making these changes, we still continue to present, as best we can, the key concepts, along with supporting interesting and relevant examples.

vi

WHAT’S NEW IN THE SEVENTEENTH EDITION?

We have made many changes to examples and exercises throughout the text. The section on “Enhancements” to our text details them. The major change to the text is in

response to user interest in the area of data analytics. Our approach is to provide instructors and students with the opportunity to combine statistical knowledge, computer

and statistical software skills, and interpretative and critical thinking skills. A set of new

and revised exercises is included at the end of chapters 1 through 18 in a section titled

“Data Analytics.”

In these sections, exercises refer to three data sets. The North Valley Real Estate

sales data set lists 105 homes currently on the market. The Lincolnville School District

bus data lists information on 80 buses in the school district’s bus fleet. The authors designed these data so that students will be able to use statistical software to explore the

data and find realistic relationships in the variables. The Baseball Statistics for the 2016

season is updated from the previous edition.

The intent of the exercises is to provide the basis of a continuing case analysis. We

suggest that instructors select one of the data sets and assign the corresponding exercises as each chapter is completed. Instructor feedback regarding student performance

is important. Students should retain a copy of each chapter’s results and interpretations

to develop a portfolio of discoveries and findings. These will be helpful as students

progress through the course and use new statistical techniques to further explore the

data. The ideal ending for these continuing data analytics exercises is a comprehensive

report based on the analytical findings.

We know that working with a statistics class to develop a very basic competence in

data analytics is challenging. Instructors will be teaching statistics. In addition, instructors will be faced with choosing statistical software and supporting students in developing or enhancing their computer skills. Finally, instructors will need to assess student

performance based on assignments that include both statistical and written components. Using a mentoring approach may be helpful.

We hope that you and your students find this new feature interesting and engaging.

vii

H OW A R E C H A P TE RS O RGA N I Z E D TO E N GAG E

DESCRIBING

DATA:

STU D E NTS A N D PRO M OTE

LE

ADISPLAYING

RN I NAND

G?EXPLORING DATA

95

INTRODUCTION

Chapter 2 began our study of descriptive statistics. In order to transform raw or ungrouped data into a meaningful form, we organize the data into a frequency distribution.

We present the frequency distribution in graphic form as a histogram or a frequency

polygon.

This

allowsrecently

us to visualize

data tend

to cluster,

the for

largest

and the

MERRILL

LYNCH

completedwhere

a studythe

of online

investment

portfolios

a sample

Each chapter begins with a set of

smallest

values,

and

general in

shape

of the

data. these data into a frequency

of clients.

For the

70the

participants

the study,

organize

)

distribution.

(See

and LO2-3.

In Chapter

3, Exercise

we first 43

computed

several

measures of location, such as the mean,

learning objectives designed to promedian, and mode. These measures of location allow us to report a typical value in the

vide focus for the chapter and motivate

set of observations. We also computed several measures of dispersion, such as the

student learning. These objectives, lorange, variance, and standard deviation. These measures of dispersion allow us to deLEARNING OBJECTIVES

cated in the margins next to the topic,

scribe the variation or the spread in a set of observations.

When you have completed this chapter, you will be able to:

We continue our study of descriptive statistics in this chapter. We study (1) dot plots,

indicate what the student should be

Summarize

qualitative(3)

variables

with frequency

tables. and statistics

(2)LO2-1

stem-and-leaf

displays,

percentiles,

and (4)and

boxrelative

plots.frequency

These charts

able to do after completing each secgive

us additional

insight into

are concentrated as well as the general

LO2-2

Display a frequency

tablewhere

using athe

bar values

or pie chart.

tion in the chapter.

shape of the data. Then we consider bivariate data. In bivariate data, we observe two

LO2-3 Summarize quantitative variables with frequency and relative frequency distributions.

variables for each individual or observation. Examples include the number of hours a

LO2-4 studied

Display aand

frequency

distribution

using

or frequency

student

the points

earned

ona histogram

an examination;

if a polygon.

sampled product meets

quality specifications and the shift on which it is manufactured; or the amount of electricity used in a month by a homeowner and the mean daily high temperature in the region

theshows

month. how

These the

charts

and graphs

provide

useful

as to

weause

business

A representative exercise opens the chapter for

and

chapter

content

can

be insights

applied

real-world

analytics to enhance our understanding of data.

situation.

Chapter Learning Objectives

Source: © rido/123RF

Chapter Opening Exercise

19

DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION

LO4-1

Construct and interpret a

dot plot.

Introduction to the Topic

DOT PLOTS

INTRODUCTION

Recall for the Applewood

Auto Group data, we summarized the profit earned on the

The

United

States automobile

retailing industry

highlyclasses.

competitive.

It is dominated

by

180 vehicles sold

with

a frequency

distribution

using iseight

When

we orgamegadealerships

that ownwe

andlost

operate

or more

franchises,

over 10,000

Each chapter starts with a review of

nized the data into

the eight classes,

the 50

exact

value

of the employ

observations.

A

people, and generate several billion dollars in annual sales. Many of the top dealerships

dot plot, on the other hand, groups

theowned

datawith

as shares

little as

possible,

andYork

weStock

do not

lose

the important concepts of the previare publicly

traded

on the New

Exchange

the identity

of an individual observation.

To develop

dot plot, we was

display

a dot(ticker

for

Lin66360_ch02_018-050.indd

18

or NASDAQ. In 2014,

the largestamegadealership

AutoNation

ous chapter and provides a link to the

symbol AN),

followedline

by Penske

Auto Group

(PAG), Group

1 Automotive,

each observation along a horizontal

number

indicating

the possible

values

of the

Inc. (ticker symbol

GPI),

and the privately

Van Tuyl

material in the current chapter. This

data. If there are identical observations

or the

observations

areowned

too close

toGroup.

be shown

These large corporations use statistics and analytics to summarize

individually, the dots are “piled”

on

top

of

each

other.

This

allows

us

to

see

theAsshape

step-by-step approach increases comand analyze data and information to support their decisions.

an exof the distribution, the value about

which

the at

data

tend to cluster,

and Itthe

largest

and

ample, we

will look

the Applewood

Auto group.

owns

four dealerprehension by providing continuity

shipsare

andmost

sells auseful

wide range

of vehicles.

the popular

smallest observations. Dot plots

for smaller

dataThese

sets,include

whereas

histoacross the concepts.

brands

Kia sets.

and Hyundai,

BMW and

sedans

luxury

grams tend to be most usefulKorean

for large

data

An example

willVolvo

show

howand

to conand a full line of Ford and Chevrolet cars and trucks.

struct and interpret dot plots.SUVs,

Ms. Kathryn Ball is a member of the senior management team at

Applewood Auto Group, which has its corporate offices adjacent to Kane

Motors. She is responsible for tracking and analyzing vehicle sales and

the profitability of those vehicles. Kathryn would like to summarize the profit earned on

the vehicles sold with tables, charts, and graphs that she would review monthly. She

E X A M P L E wants to know the profit per vehicle sold, as well as the lowest and highest amount of

profit. She is also interested in describing the demographics of the buyers. What are

The service departments

at many

Tionesta

Ford

and Sheffield

their ages? How

vehicles

haveLincoln

they previously

purchasedMotors

from oneInc.,

of thetwo

Appleof the four Applewood

Auto Group

were

both open 24 days last

wood dealerships?

What typedealerships,

of vehicle did they

purchase?

The Applewood

Auto Group

operates four

dealerships:

month. Listed below

is the number

of vehicles

serviced

last month at the two

Source: © Justin Sullivan/Getty Images

Example/Solution

After important concepts are introduced,

a solved example is given. This example

provides a how-to illustration and shows

a relevant business application that

helps students answer the question,

“How can I apply this concept?”

dealerships. Construct

dot

plots

andsells

report

summary

statistics

to compare the

• Tionesta

Ford

Lincoln

Ford and

Lincoln cars

and trucks.

• Olean Automotive Inc. has the Nissan franchise as well as the General Motors

two dealerships.

brands of Chevrolet, Cadillac, and GMC Trucks.

• Sheffield Motors Inc. sells Buick, GMC trucks, Hyundai, and Kia.

• Kane Motors offers

the Chrysler,

Dodge, and Jeep line as well as BMW and Volvo.

Tionesta

Ford Lincoln

Monday

month, Ms. Ball

collects data

from each

of the four dealerships

Tuesday Every

Wednesday

Thursday

Friday

Saturday

and enters them into an Excel spreadsheet. Last month the Applewood

23

30

CHAPTER294

106

33Auto Group27

28 at the 39

26

sold 180 vehicles

four dealerships.

A copy of the first

32few observations

28 appears 33

35 variables

32collected include:

to the left. The

25 • Age—the

36 age of the buyer

31 at the 32

27

time of the purchase.

32 • Profit—the

35 amount earned

37

36 dealership

30 on the sale of each

by the

35

vehicle.

calculate quartiles. Excel

and Excel

2016 offer

both

The

Excel function,

• 2013

Location—the

dealership

where

themethods.

vehicle was

purchased.

Quartile.exc, will result

the same

answer sedan,

as Equation

4–1.

The or

Excel

function, Quar •in Vehicle

type—SUV,

compact,

hybrid,

truck.

•Excel

tile.inc, will result in the

Method answers.

Previous—the

number of vehicles previously purchased at any of the

Self-Reviews

Self-Reviews are interspersed

throughout each chapter and

follow Example/Solution sections. They help

students monLin66360_ch04_094-131.indd

95

itor their progress and provide

immediate reinforcement for

that particular technique. Answers are in Appendix E.

four Applewood dealerships by the consumer.

SELF-REVIEW

The entire data set is available at the McGraw-Hill website (www.mhhe

.com/lind17e) and in Appendix A.4 at the end of the text.

4–2

The Quality Control department of Plainsville Peanut Company is responsible for checking

CONSTRUCTING FREQUENCY TABLES

LO2-1

the weight of the 8-ounce jar of peanut butter. The weights of a sample of nine jars proSummarize qualitative

duced last hour are:

Recall from Chapter 1 that techniques used to describe a set of data are called descrip1/10/17 7:41 PM

variables with frequency

tive statistics. Descriptive statistics organize data to show the general pattern of the

and relative frequency

7.72where

7.8values

7.86tend 7.90

7.94

7.97

8.06

8.09

data, 7.69

to identify

to concentrate,

and to expose

extreme or unusual

tables.

data values. The first technique we discuss is a frequency table.

(a) What is the median weight?

(b) Determine

the weights

corresponding

first anddata

thirdinto

quartiles.

FREQUENCY

TABLE

A groupingtoofthe

qualitative

mutually exclusive and

collectively exhaustive classes showing the number of observations in each class.

EXERCISES

11.

viii

Determine the median and the first and third quartiles in the following data.

46

Lin66360_ch02_018-050.indd 19

12.

47

49

49

51

53

54

54

55

55

59

Determine the median and the first and third quartiles in the following data.

1/6/17 4:52 AM

1/6/17 4:52 AM

(c)

Are the events in part (a)(i) complementary or mutually ex

The probability of passing both is .50. What is the probability of passing at least one?

21. The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green

The General Rule of Addition

swordtails (44 female and 36 male) and 60 are orange swordtails (36 female and

24 males). A fish is randomly captured from the aquarium:

a. What is the probability the selected

fish is a green

may not be mutually exclu

The outcomes

of answordtail?

experiment

b. What is the probability the selected

is male? selected a sample of 200 tourists wh

Tourist fish

Commission

c. What is the probability the selected

fishsurvey

is a male

green swordtail?

year. The

revealed

that 120 tourists went to Disney

d. What is the probability the selected fish is either a male or a green swordtail?

Gardens near Tampa. What is the probability that a person

22. A National Park Service survey of visitors to the Rocky Mountain region revealed

or Busch

Gardens?

If the

that 50% visit Yellowstone Park,World

40% visit

the Tetons,

and 35%

visitspecial

both. rule of addition is use

a touristwill

who

to Disney

Worldattractions?

is .60, found by 120/200

a. What is the probability a vacationer

visitwent

at least

one of these

tourist going to Busch Gardens is .50. The sum of these p

b. What is the probability .35 called?

however,

that this probability cannot be greater than 1. The

c. Are the events mutually exclusive?

Explain.

Statistics in Action

STATISTICS IN ACTION

ists visited both attractions and are being counted twice! A c

revealed that 60 out of 200 sampled did, in fact, visit both a

that you believe that at

bility of visiting both. Thus:

A SURVEY OF PROBABILITY CONCEPTS

145

LO5-4

To answer our question, “What is the probability a se

If you wish to get some

Calculate probabilities

Disney

World

or

Busch

Gardens?”

(1)

add

the

probability

attention at the next gathStatistics in Action articles are

usingscattered

the rules of throughWorld and the probability he or she visited Busch Garden

ering

you

attend,

announce

multiplication.

out the text, usually about two per chapter. They

In this section, we discuss the rules for computing the likelihood that two events both

RULES OF MULTIPLICATION

TO CALCULATE PROBABILITY

happen, or their joint probability.

example, 16%

of the

2016 tax returns were preprovide unique, interesting applications and hisP(Disney)For

= .60

P(Busch)

= .50

least two people present

P(Disney

Busch) What

= P(Disney)

+ P(Busch) − P(bo

pared by H&R Block and 75% of those returns

showedor

a refund.

is the likelihood

torical insights in the field of statistics.

weretax

born

on the

same

a person’s

form

was

prepared by H&R Block and the person received a refund?

= .60 + .50 − .30 = .80

64

Definitions

Definitions of new terms or terms unique to

the study of statistics are set apart from the

text and highlighted for easy reference and

review. They also appear in the Glossary at

the end of the book.

Formulas

Formulas that are used for the first time are

boxed and numbered for reference. In addition, a formula card is bound into the back of

the text that lists all the key formulas.

Exercises

date—thatillustrate

is, the same

Venn diagrams

this as the intersection of two events. To find the likelihood of

day of

the year butwe

notuse the rules of

When

two events

both

the probability

two events

happening,

multiplication.

There

areoccur,

two rules

of multipli- is called

necessarily

same

ability

cation: the

specialthe

rule

andyear.

the general

rule.(.30) that a tourist visits both attractions is an examp

If there are 30 people in

the room,

the of

probability

of

Special

Rule

Multiplication

a duplicate is .706. If there

The special

rule

of

multiplication

are

60 people3in the room, requires that two events A and B are independent.

CHAPTER

P(Disney

and Busch)

= .30

Two events

are independent

if the

occurrence

of one

event does not alter the probabilthe probability

is .994 that

ity of theatoccurrence

of the

least two people

shareother

the event.

same birthday. With as few

INDEPENDENCE

The

one of

event

has nounemployment

effect on therates?

probability of

a. What

isoccurrence

the arithmeticofmean

the Alaska

as 23 people

the

chances

JOINT

PROBABILITY

probability

that measures the likelihood two or more

the

occurrence

of

another

event.

Find

theAthat

median

are even,b.that

is .50,

at and the mode for the unemployment rates.

events will happen

concurrently.

Compute

least two c.people

sharethe

thearithmetic mean and median for just the winter (Dec–Mar) months.

Is it much different?

birthday.

Hint:

To

Onesame

way

to

think

about

independence

to assume

events A

and Bfor

occur

22.

Big Orange Trucking is is

designing

an that

information

system

use at

in differ“in-cab”

ent times.

For

example,

when

event

B occurs

after

event

A

occurs,

does

A have any

this, find

the

communications.

It must

summarize

data

from

eight sites

a region

So compute

the

general

rule

of addition,

which

is used

to

compute

thethroughout

probability

ofeffect

twoto

on

the likelihood

that

event

Bexclusive,

occurs?

Ifis:

the

answer

no, then measure

A and B of

are

independent

typical

conditions.

Compute

an is

appropriate

central

location for

probability

everyone

was

events

that

are describe

not

mutually

the

variables

wind

direction,

temperature,

and

pavement.

events. To

illustrate

independence,

The outcome of a coin

born

on a different

day and suppose two coins are©tossed.

Rostislav Glinsky/Shutterstock.com

toss (head

tail)

is unaffected

useorthe

complement

rule.by the outcome of any other prior coin toss (head or tail).

City

Wind

Direction

Temperature

Pavement

For Try

twothis

independent

events A and B,The

the probability

that A and B shows

will both

occur

is that are n

Venn

events

in your

class.

GENERAL

RULE

OF

ADDITION

P(A or following

B) = P(A) +

P(B)diagram

− P(A and B) two[5–4]

West

89the

found by multiplying Anniston,

the twoALprobabilities.

This

is thetospecial

rule

ofjoint

multiplication

events

overlap

illustrate

eventDry

that and

some people h

Atlanta,

Northwest

86

Wet

is written symbolically

as: GA

Augusta, GA

Southwest

92

Wet

For the expression

P(A or AL

B), the wordSouth

or suggests that A may

Birmingham,

91 occur or B may

Dry occur.

This

also includes

the

possibility

that A and

B may

This

use of or is sometimes

SPECIAL

RULE OF

MULTIPLICATION

P(Aoccur.

and B)

=92

P(A)P(B)

Jackson,

MS

Southwest

Dry[5–5]

called an inclusive. You

could

or B or both) to emphasize

that theTrace

union of

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MS also write P(A

South

92

the events includes the

intersection

of A and

B.

Monroe,

LA

Southwest

93

Wet

If we compare the

general

rules of addition, the

is

Tuscaloosa,

AL and special

Southwest

93 important difference

Trace

determining if the events are mutually exclusive. If the events are mutually exclusive, then

the joint

probability DATA:

P(A and

B) is 0 andMEASURES

we could use the special rule of addition. OtherDESCRIBING

NUMERICAL

79

wise, we must account for the joint probability and use the general rule of addition.

Software Solution

Lin66360_ch05_132-174.indd 144

Exercises are included

after sec-147 E X E R C I S E SE X A M P L E

Lin66360_ch05_132-174.indd

1/10/17 7:41 PM

47–52, do the following:

What isFor

theExercises

probability

that a card chosen at random from a standard deck of cards

tions within the chapter and at

E

X

A

M

P

L

E

a. Compute

sample variance.

will be either

a king orthe

a heart?

the end of the chapter. Section

b. Determine the sample standard deviation.

Table 2–4 on page 26 shows the profit on the sales of 180 vehicles at Applewood

47.

Consider

these

values

a sample: 7, 2, 6, 2, and 3.

exercises cover the material studAuto Group. Determine the mean and the median selling price.

48.

SOLU

T IThe

O Nfollowing five values are a sample: 11, 6, 10, 6, and 7.

ied in the section. Many exercises

49.

Dave’s Automatic Door, referred to in Exercise 37, installs automatic garage

openers.

on a sample,

times, in minutes,

required

We may bedoor

inclined

to addBased

the probability

of afollowing

king andare

thethe

probability

of a heart.

But thisto

have data files available to import

S

O

L

U

T IIfdoor

Owe

N openers:

install 10

28, 32,

44, 40,

54, 38, 32,

and

creates a problem.

do that, the

king24,

of 46,

hearts

is counted

with

the42.

kings and also

into statistical software. They are

Theifsample

of eight

companies

in the aerospace

industry,

to in

with the50.

hearts.

So,

we

simply

addmodal

the probability

king (there

are 4referred

in aindeck

ofExer52

The mean,

median,

and

amountsofofa profit

are reported

the following

cise

38, was of

surveyed

as

to their

return

on

investment

last year.

The results

are

indicated with the FILE icon.

cards) to the

probability

a heart

(there

are shot).

13 in a(Reminder:

deck

of 52The

cards)

and report

17

output

(highlighted

in the

screen

instructions

tothat

create

the

10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

out

of

52

cards

meet

the

requirement,

we

have

counted

the

king

of

hearts

twice.

We

output

appear

in

the

Software

Commands

in

Appendix

C.)

There

are

180

vehicles

Answers to the odd-numbered

51.

The Houston, Texas, Motel Owner Association conducted a survey regarding

need to subtract

1 card

17

theListed

king below

ofbehearts

is counted

once.

inweekday

the study,

sofrom

using

aincalculator

would

tedious

and prone

tobusiness-class

error. Thus,

motel

ratesthe

the so

area.

is the

room

rateonly

for

exercises are in Appendix D.

there are 16 cards that are either hearts or kings. So the probability is 16/52 = .3077.

We can use a statistical software package to find many measures of location.

guests for a sample of 10 motels.

Card

$101

$97

$103

$110

Probability

$78

$87

$101

$80

Explanation

$106

$88

A consumer

organization is

concerned

credit card debt. A

P(A)watchdog

= 4/52

4 kings

in a deckabout

of 52 cards

survey of 10 young

debt

of more

than

$2,000

Heart

P(B) adults=with

13/52credit card13

hearts

in a deck

of 52

cards showed they

paid

an averageP(A

of and

justB)over

$100 per month

balances.

Listed below

King

of Hearts

= 1/52

1 king ofagainst

hearts intheir

a deck

of 52 cards

are the amounts each young adult paid last month.

52.King

Computer Output

$110

$126

$103

$93

$99

$113

$87

The text includes many software examples, using

Excel, MegaStat®, and Minitab. The software results are

LO3-5 for a particular

illustrated in the chapters. Instructions

INTERPRETATION AND USES

software example are in AppendixExplain

C. and apply

Chebyshev’s theorem

OF THE STANDARD DEVIATION

and the Empirical Rule.

Lin66360_ch05_132-174.indd 145

STATISTICS IN ACTION

Most colleges report the

“average class size.” This

information can be mislead-

$101

$109

$100

The standard deviation is commonly used as a measure to compare the spread in two

or more sets of observations. For example, the standard deviation of the biweekly

amounts invested in the Dupree Paint Company profit-sharing plan is computed1/10/17

to be 7:41 PM

$7.51. Suppose these employees are located in Georgia. If the standard deviation for a

group of employees in Texas is $10.47, and the means are about the same, it indicates

that the amounts invested by the Georgia employees are not dispersed as much as

those in Texas (because $7.51 < $10.47). Since the amounts invested by the Georgia

employees are clustered more closely about the mean, the mean for the Georgia emix

ployees is a more reliable measure than the mean for the Texas group.

Chebyshev’s Theorem

We have stressed that a small standard deviation for a set of values indicates that these

she estimates that the probability is .025 that an applicant will not be able to repay

his or her installment loan. Last month she made 40 loans.

a. What is the probability that three loans will be defaulted?

b. What is the probability that at least three loans will be defaulted?

34. Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per

minute. The distribution of arrivals approximates a Poisson distribution.

a. What is the probability that no automobiles arrive in a particular minute?

b. What is the probability that at least one automobile arrives during a particular

minute?

35. It is estimated that 0.5% of the callers to the Customer Service department of Dell

Inc. will receive a busy signal. What is the probability that of today’s 1,200 callers at

least 5 received a busy signal?

36. In the past, schools in Los Angeles County have closed an average of 3 days each

year for weather emergencies. What is the probability that schools in Los Angeles

County will close for 4 days next year?

H OW DO E S TH I S TE X T R E I N FO RC E

STU D E NT LE A R N I N G?

BY C H A P TE R

CHAPTER SUMMARY

348

I. A random

CHAPTER

10variable is a numerical value determined by the outcome of an experiment.

244

168

1. The probability of making a Type

error is equal to the level of significance. (6–1)

μ =I Σ[xP(x)]

CHAPTER

7 probability is designated by the Greek letter α.

2. This

B. The

variance is equal to:

CHAPTER

5 II error occurs when a false null hypothesis is not rejected.

B. A Type

= Σ[(x

− μ)2isP(x)]

1. The probability of making aσ2Type

II error

designated by the Greek letter β. (6–2)

II. A probability distribution is a listing of all possible outcomes of an experiment and the

probability associated with each outcome.

A. A

discrete

distribution

assume only

The

majorprobability

characteristics

of the can

t distribution

are:certain values. The main features are:

1.

of the probabilities

1. The

It is asum

continuous

distribution.is 1.00.

2.

The

probability

of

a

particular

outcome

is

between

0.00 and 1.00.

2. It is mound-shaped and symmetrical.

3.

outcomes

are mutually

exclusive.

3. The

It is flatter,

or more

spread out,

than the standard normal distribution.

B. A

continuous

distribution

can

assume

an

infinite

number

of valuesofwithin

a specific

range.

4. There is a family of t distributions, depending on the number

degrees

of freedom.

III.

mean

and types

variance

of a probability

distribution

V. The

There

are two

of errors

that can occur

in a testare

of computed

hypothesis.as follows.

A.

mean

is equal

to:when a true null hypothesis is rejected.

A. The

A Type

I error

occurs

Chapter Summary

Each chapter contains a brief summary

of the chapter material, including vocabulary, definitions, and critical formulas.

Pronunciation Key

This section lists the mathematical symbol,

its meaning, and how to pronounce it. We

believe this will help the student retain the

meaning of the symbol and generally enhance course communications.

Chapter Exercises

2. The likelihood

of a Type

II errorthe

must

be calculated

comparing

thelimits

hypothesized

68. In establishing

warranties

on HDTVs,

manufacturer

wants

to set the

so that few

distribution to an alternate distribution based on sample results.

need repair at the manufacturer’s expense. On the other hand, the warranty period

P R O N U N C I A T I O Nwill

K

EY

must be long enough to make the purchase attractive to the buyer. For a new HDTV, the

mean number of MEANING

months until repairs are needed is 36.84 with a standard

deviation of

SYMBOL

PRONUNCIATION

P R O N U N C I A T I O N3.34Kmonths.

E Y Where should the warranty limits be set so that only 10% of the HDTVs

Lin66360_ch06_175-208.indd 202

CHAPTER

CHAPTER

Generally, the end-of-chapter exercises

are the most challenging and integrate

the chapter concepts. The answers and

worked-out solutions for all oddnumbered exercises are in Appendix D

at the end of the text. Many exercises

are noted with a data file icon in the

margin. For these exercises, there are

data files in Excel format located on the

text’s website, www.mhhe.com/Lind17e.

These files help students use statistical

software to solve the exercises.

Data Analytics

The goal of the Data Analytics sections is to develop analytical skills.

The exercises present a real world

context with supporting data. The data

sets are printed in Appendix A and

available to download from the text’s

website www.mhhe.com/Lind17e. Statistical

software is required to analyze the data

and respond to the exercises. Each data

set is used to explore questions and discover findings that relate to a real world

context. For each business context, a

story is uncovered as students progress

from chapters one to seventeen.

x

DATA ANA

P(A)

Probability of A

P of A

need repairs at the manufacturer’s expense?

SYMBOL

MEANING

P(∼A)

Probability

not A

P of not Aselects

69.

DeKorte Tele-Marketing

Inc. of

is considering

purchasing a machine thatPRONUNCIATION

randomly

H0 and

hypothesis

and B)

automaticallyProbability

dialsNull

telephone

numbers.

DeKorte Tele-MarketingHmakes

P(A

of A and

B

Psub

of zero

Amost

and Bof its

calls

so of

calls

toBbusiness phones are wasted. The

manufacturer

of

H1 or

Alternate

H Psub

P(A

B) during the evening,

Probability

Ahypothesis

or

of one

A or B

the machine claims that its programming reduces the calling to business phones to 15%

α/2| B)

Two-tailed

significance

level

Alpha

divided

P(A

Probability

of the

A given

B has

P of A

given by

Bthe2

of all calls. To test

this claim,

director

ofhappened

purchasing at DeKorte programmed

xP

Limit of of

then sample

mean r at a time

x bar

Permutation

items selected

Pnr sub c

n cr machine to select a sample of 150 phone numbers. What is the likelihood that more

numbersofselected

aremean

thoser of

assuming

the manuAssumed

population

muCnr

sub zero

μC than 30 of the phone

Combination

n items selected

at abusinesses,

time

n 0r

facturer’s claim is correct?

70. A carbon monoxide detector in the Wheelock household activates once every 200 days

average.

E X E R ConI S

E S Assume this activation follows the exponential distribution. What is the

E X E R Cprobability

I S E S that:

There will

alarm

within

the nextthe

60 mean

days? gross income of plumbers in the Salt

25. a.

According

tobe

theanlocal

union

president,

47. b.

The

department

atthe

Pepsico

plans to survey

about a newly

Atmarketing

least

400research

days will

pass

before

nextdistribution

alarm?

Lake

City area

follows

the

normal

probability

with ateenagers

mean of $45,000

and a

developed

soft

drink.

Each

will250

be

asked

to compare

with his for

or her

favorite

soft drink.

c.

It will be

between

and

days until

the nextitwarning?

standard

deviation

of150

$3,000.

A recent

investigative

reporter

KYAK

TV found,

for a

a.

What

is

the

experiment?

d.

Find the

median

time until

next

activation.

sample

of 120

plumbers,

thethe

mean

gross

income was $45,500. At the .10 significance

b.

What

one

event?thethat

71. “Boot

time”

(thepossible

time between

appearance

the Bios

screen

toto

the

first file that

is

level,

is itisreasonable

to conclude

the meanofincome

is not

equal

$45,000?

Deter48. loaded

The

of timesona Eric

particular

event

occurred

in the past

is divided

by the number

of

in Windows)

Mouser’s

personal

computer

follows

an exponential

distribuminenumber

the

p-value.

occurrences.

What

is

this

approach

to

probability

called?

tion

with

a

mean

of

27

seconds.

What

is

the

probability

his

“boot”

will

require:

Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a

26.

49. a.

The

probability

the cause

and the cure

for allthat

cancers

will be discovered

before

the

Less

than 15

seconds?

long

history,

thethat

production

department

reports

the distribution

of the bag

weights

year

2020

isnormal

.20.

What

viewpoint

of the

probability

does

this statement

illustrate?process is

b.

More

than

60 seconds?

follows

the

distribution

and

standard

deviation

of the packaging

Berdine’s

Chicken

Factory

several

stores

in the

Head,manager,

South Carolina,

50. c.

Between

30bag.

and

45the

seconds?

3 pounds

per

At

end of has

each

day, Jeff

Rutter,

theHilton

production

weighs

c. In thed.

dialog

box,

that thebelow

range of

Variable

1 isweight

area.

When

interviewing

applicants

for

server

positions,

the

owner

like to inWhat

isindicate

the

point

which

only

10%

ofofthe

boots

occur?

10

bags

and

computes

the

mean

the

sample.

Below

arewould

the weights

of

from A1

to A6 information

and Variable 2 from

to B7,

the Hypotheclude

onB1

the

of tip a server

to earn

per

check popula(or bill).

72.

between

visits

toamount

aAlpha

U.S.is emergency

roomcan

forexpect

a member

of the

general

10 bags

fromistoday’s

production.

sizedThe

Meantime

Difference

0, click

Labels,

0.05,

A Output

study

of 500

recent

indicated

server

theWhat

following

amounts

in

and the

Range

is D1.

Click OK. checks

tion

follows

an

exponential

distribution

withthe

a mean

ofearned

2.5 years.

proportion

of the

tips per 8-hour shift.

population:

45.6

47.7

47.6

46.3

46.2

47.4

49.2

55.8

47.5

48.5

a. Will visit an emergency room within the next 6 months?

b. Will not visit the ER over

theofnext

6 years?

Amount

a. Can Mr. Rutter conclude

that Tip

the mean weight ofNumber

the bags is less than 50 pounds?

c. Will visit an ER next year, but not this year?

Use the .01 significanceuplevel.

to $ 20

d. Find the first and third$0quartiles

of this distribution. 200

b. In a brief report, tell why

Mr.

the z distribution

as the test statistic.

20 upon

to aRutter

50 can use

100 an exponential

73. The times between failures

personal

computer follow

distribution

c. Compute the p-value.50 up to 100

75

with a mean of 300,000 hours. What is the probability of:

27. A new weight-watching100

company,

Weight Reducers International,

advertises that those

up to hours?

200

75

a. A failure in less than 100,000

who join will lose an average

of 10 pounds after the first

two weeks. The standard devior more

b. No failure in the next200

500,000

hours? CHAPTER 12 50

ation is 2.8 pounds. A random sample of

50 The

people

who joined

theof weight

reduction

12–1.

Excel350,000

commands

for

the test

variances on

page 391 are:

c. The next failure occurring

between 200,000

and

hours?

Total

datalevel

for U.S.of

25significance,

in column A and for

I-75we

in colprogram revealed a mean

loss of 9 pounds.a.AtEnter

thethe500

.05

can

d. What are the mean and standard deviation of umn

theB.time

failures?

Labelbetween

the two columns.

conclude that those joining Weight Reducers b.

willSelect

losethe

less

than

10

pounds?

Determine

Data tab on the top menu. Then, on the far right,

theWhat

p-value.

a.

is the probability of a tip of $200 or more?

select Data Analysis. Select F-Test: Two-Sample for

L Y T I 28.

C Sb.

thenof

click

OK.

Dole

Inc. is“$0

concerned

that“$20

the 16-ounce

sliced

pineapple mutually

is being

ArePineapple

the categories

up to $20,”

up toVariances,

$50,”can

and

so

on considered

c. The range of the first variable is A1:A8, and B1:B9 for the

overfilled.

Assume

the standard

deviation

of thesecond.

process

is

ounce.

The

quality-conexclusive?

Clickwww.mhhe.com/lind17e.)

on .03

Labels,

enter 0.05

for Alpha,

select D1 for

11–2. The

Minitab

commands

for

the

two-sample

t-test

on

page

368

(The data for these exercises are available at the text website:

thewere

Output

Range, and

click

OK.arithmetic

trolIfdepartment

tookassociated

a randomwith

sample

50 cans

and totaled,

found

that

the

mean

are:

c.

the probabilities

eachofoutcome

what

would

that total

be?

a. Put theweight

amount absorbed

by the Store

brand inAt

C1 the

and the

was

16.05

ounces.

5%

level

of

significance,

can we conclude

thatsold

the

d.

What

is

the

probability

of

a

tip

of

up

to

$50?

74.

Refer

to

the

North

Valley

Real

Estate

data,

which

report

information

on

homes

amount absorbed by the Name brand paper towel in C2.

mean

weight

greater

than

ounces?

Determine

e.

theis

probability

of a16

tip

of

less than

$200? the p-value.

theis

last

year.

b. Fromduring

the What

toolbar,

select

Stat,

Basic Statistics,

and

then

2-Sample,

and click

51.

Winning

allOK.three

Crown”

races of

is the

considered

thecomputed

greatestearlier

feat of

a.

The

mean

selling“Triple

price (in

$ thousands)

homes was

toabepedigree

$357.0,

c. In the next dialog box, select Samples in different colAfter

adeviation

successful

Kentucky

Derby,

Corn on

the Cob to

is estimate

a heavy favorite

at 2

with

standard

ofC2$160.7.

the normal

distribution

the percentumns,racehorse.

select

C1aStore

for the First

column and

Name of Use

the Second,

click

nextselling

to Assume

variances,

to 1

odds

toboxwin

the

Preakness

Stakes.

age

ofthe

homes

forequal

more

than $500.000. Compare this to the actual results. Is price

and click OK.

a. normally

If he is adistributed?

2 to 1 favorite

to win the

Belmont

as well,

what ishow

his probability

of

Try another

test.

If price Stakes

is normally

distributed,

many homes

winning

the aTriple

should

have

price Crown?

greater than the mean? Compare this to the actual number of homes.

b. Construct

What do a

his

chancesdistribution

for the Preakness

Stakes

to be in order for him to be

frequency

of price. What

do have

you observe?

“even

money”

to on

earn

themarket

Triple Crown?

b. The

mean

days

the

is 30 with a standard deviation of 10 days. Use

52. Thethe normal

first card selected

fromtoaestimate

standardthe

52-card

deck

a king.on the market more than

distribution

number

of ishomes

a. 24 days.

If it is returned

to the

is the

probability

that atest.

kingIfwill

beon

drawn

on the

Compare

thisdeck,

to thewhat

actual

results.

Try another

days

the market

second selection?

is normally

distributed, how many homes

should

be

on the market more than the

12–2. The Excel commands for the one-way ANOVA on page 400 are:

b. mean

If the number

king is not

replaced,

whatthis

is the

probability

that

king

will labeled

be

drawn

onWTA,

thePoof days?

Compare

to the

actual

of

homes.

Does

the normal

a. Key innumber

data

intoafour

columns

Northern,

cono, and Branson.

second selection?

Software Commands

Lin66360_ch10_318-352.indd 348

Software examples using Excel, MegaStat®, and Minitab are included throughout the text. The explanations of the

computer input commands are placed at

the end of the text in Appendix C.

Lin66360_ch07_209-249.indd 244

Lin66360_ch05_132-174.indd 168

11–3. The Excel commands for the paired t-test on page 373 are:

a. Enter the data into columns B and C (or any other two columns) in the spreadsheet, with the variable names in the

first row.

b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select t-Test: Paired Two Sample for

Means, and then click OK.

c. In the dialog box, indicate that the range of Variable 1 is

from B1 to B11 and Variable 2 from C1 to C11, the

Hypothesized Mean Difference is 0, click Labels, Alpha is

.05, and the Output Range is E1. Click OK.

1/14/17 7:02 AM

1/16/17 9:53 PM

b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select ANOVA: Single Factor, then

click OK.

c. In the subsequent dialog box, make the input range A1:D8,

click on Grouped by Columns, click on Labels in first row,

the Alpha text box is 0.05, and finally select Output Range

as F1 and click OK.

1/14/17 8:29 AM

1/10/17 7:41 PM

780

Lin66360_appc_774-784.indd 780

1/20/17 10:28 AM

126

A REVIEW OF CHAPTERS 1–4

D A T A A N A LY T I C S

44.

Refer to the North Valley real estate data recorded on homes sold during the last

year. Prepare a report on the selling prices of the homes based on the answers to the

following questions.

a. Compute the minimum, maximum, median, and the first and the third quartiles of

price. Create a box plot. Comment on the distribution of home prices.

b. Develop a scatter diagram with price on the vertical axis and the size of the home on

the horizontal. Is there a relationship between these variables? Is the relationship

16–7 direct

a. or indirect?

c. For homes without a pool, develop a scatter

Rank diagram with price on the vertical axis

and the size of the home on the horizontal. Do the same for homes with a pool. How

2

do the relationships

between

price

x

y

x and size fory homes without

d a pool anddhomes

with a pool compare?

Refer 805

to the Baseball

that report information

on

League

45.

232016 data5.5

1

4.5the 30 Major

20.25

Baseball teams for the 2016 season.

777

62 opened, 3.0

9 of operation

−6.0for that stadium.

36.00 For

a. In the data

set, the year

is the first year

each team, use this variable to create a new variable, stadium age, by subtracting

820

60

8.5

8

0.5

0.25

the value of the variable, year opened, from the current year. Develop a box plot

with the 682

new variable,40

age. Are there

which of the stadiums

1.0 any outliers?

4 If so, −3.0

9.00 are

outliers?

777

70 create3.0

−7.0

49.00 the

b. Using the

variable, salary,

a box plot. 10

Are there any

outliers? Compute

quartiles810

using formula

of your

28(4–1). Write

7.0a brief summary

2

5.0analysis. 25.00

c. Draw a scatter diagram with the variable, wins, on the vertical axis and salary on the

805

30 your conclusions?

5.5

3

2.5

6.25

horizontal

axis. What are

d. Using the variable, wins, draw a dot plot. What can you conclude from this plot?

840

42

10.0

5

5.0

25.00

Refer to the Lincolnville School District bus data.

46.

a. Referring777

to the maintenance

cost3.0

variable, develop

plot. What are16.00

the mini55

7 a box

−4.0

mum, first quartile, median, third quartile, and maximum values? Are there any

51

8.5

6

2.5

6.25

outliers?820

b. Using the median maintenance cost, develop a contingency0table with bus

manufac193.00

turer as one variable and whether the maintenance cost was above or below the

median as the other variable. What are your conclusions?

Answers to Self-Review

The worked-out solutions to the Self-Reviews are provided at the end of the text in Appendix E.

17

17

6(193)

= −.170

10(99)

b. H0: ρ = 0; H1: ρ ≠ 0. Reject H0 if t < −2.306 or t > 2.306.

rs = 1 −

BY S E C TI O N

t = −.170√

Section Reviews

A REVIEW OF

China

A REVIEW OF CHAPTERS

1–4Produced 832.8% more steel than the US

130

CASES

The review also includes continuing

cases and several small cases that let

students make decisions using tools

and techniques from a variety of

chapters.

Practice Test

The Practice Test is intended to

give students an idea of content

that might appear on a test and

how the test might be structured.

The Practice Test includes both

objective questions and problems

covering the material studied in

the section.

*

CHAPTER 17

*

This section is a review of the

and terms

introduced in Chapters 1–4. Chapter 1 began by describing the

5.major

Referconcepts

to the following

diagram.

meaning and purpose of statistics. Next we described the different types of variables and the four levels of measurement.

Chapter 2 was concerned with describing a set of observations by organizing it into a frequency distribution and then

portraying the frequency distribution as a histogram or a frequency polygon. Chapter 3 began by describing measures of

location, such as the mean, 17–1

weighted mean,

1. median, geometric mean, and mode. This chapter also included measures of

dispersion, or spread. Discussed in this section

were the range,Amount

variance, and Index

standard

deviation. Chapter 4 included

Country

(Based=US)

several graphing techniques such as dot plots, box plots, and scatter diagrams. We also discussed the coefficient of skew0

40

80

160

ness, which reports the lack of symmetry in a China

set of data.

822.7120

932.8 200

Throughout this section we stressed the importance of statistical software, such as Excel and Minitab. Many computer

110.7

125.5

a. What ishow

theJapan

graph called?

outputs in these chapters demonstrated

quickly

and effectively a large data set can be organized into a frequency

b. What

the

median,

and first

third quartile

values?

United

States

88.2

100.0

distribution, several of the measures

of are

location

or measures

of and

variation

calculated,

and

the information presented in

c. Is the distribution positively skewed? Tell how you know.

graphical form.

India

86.5

98.1

d. Are there any outliers? If yes, estimate these values.

Russia the number of71.5

81.1

e. Can you determine

observations in the study?

After selected groups of chapters

(1–4, 5–7, 8 and 9, 10–12, 13 and

14, 15 and 16, and 17 and 18), a

Section Review is included. Much

like a review before an exam, these

include a brief overview of the chapters and problems for review.

Cases

10 − 2

= −0.488

1 − (−0.170) 2

A REVIEW OF CHAPTERS 1–4

129

H01–4

is not rejected. We have not shown a relationship

CHAPTERS

between the two tests.

17

17

2. a.

location,

charts

or draw graphs

2. There

Determine

thesales

mean

and median ofwho

the checking

markets.

are 40

representatives

call di- acA. create

Century

National

Banksuch as a cumulative frequency

distribution,

determine

the quartiles

count

balances.

Compare

theIndex

and thedemedian

on large-volume

customers,

such

asmean

the athletic

The following

case willand

appear

inYear

subsequent

reviewAverage

sec- rectlyHourly

Earnings

(1995

=

Base)

for both

men

and

women.

Develop

the

charts

and

write

balances

for

the

four

branches.

Is

there

a difference

partments

at

major

colleges

and

universities

and

tions. Assume that you work in the Planning Department of

the report

summarizing

theBank

yearly

employees

among

thefranchises.

branches? There

Be sureare

to 30

explain

the

difference

sports

sales

reprethe Century

National

andsalaries

report

Lamberg. You professional

1995toof Ms.

11.65

100.0

at Wildcat

Plumbing

Supply.

Does it appear that there are

the mean

the median

in your

report.

sentatives between

who represent

theand

company

to retail

stores

lowill need

to do some

Lin66360_ch04_094-131.indd

126data analysis and prepare a short writ2000

14.02

120.3

pay differences

on gender?

3. shopping

Determine

the and

range

and discounters

the standard

deviation

of

malls

large

such

as

ten report. based

Remember,

Mr. Selig is the president of the bank, cated in

the

checking

account

balances.

What

do

the

and Target.

2005

138.5first and

so you will

want to ensure

that your

report is complete and Kmart 16.13

C. Kimble

Products:

Is There

a Difference

quartiles

show? Determine

the the

coefficient

of

Upon third

his return

to corporate

headquarters,

CEO

accurate. A copy of the data appears

in

Appendix

A.6.

2013

19.97

171.4

In the

Commissions?

andfor

indicate

it shows.

Because

sales manager

a reportwhat

comparing

the comCentury National Bank has offices in several cities in asked the skewness

At thethe

January

national

sales

meeting,

the

CEO

of

Kimble

Mr. Selig

does

not

deal

with

statistics

daily,

include

a

2016

21.37

183.4

missions

earned

last

year

by

the

two

parts

of

the

sales

Midwest and the southeastern part of the United

Products

wasMr.

questioned

extensively

com-like to team. The brief

description

and interpretation

the standard

information

is reported

below. Write of

a brief

reStates.

Dan Selig,

presidentregarding

and CEO,the

would

pany policy

for

paying

commissions

to

its

sales

represen2016

Average

wage

Increased

83.4%

from

1995

deviation

and

other

measures.

port.

Would

you

conclude

that

there

is

a

difference?

Be

know the characteristics of his checking account customtatives.

The

company

sells sporting

goods

to two major

sure to include information in the report on both the ceners.

What

is the balance

of a typical

customer?

B. Wildcat Plumbing Supply Inc.:

How many other bank services do the checking

ac- tral tendency and dispersion of the two groups.

b.

Do We Have Gender Differences?

Commissions

Earned by Sales

count customers

use?Representatives

Do the customers use the ATM serWildcat Earned

Plumbing

Supply

has served the plumbing

Calling

on and,

Athletic

Departments

($) WhatYear

Commissions

by Sales

Representatives

vice

if so,

how often?

about debit cards?

Who Hourly

Average

Earnings

Index

(1995 – 2000 = Base)

needs

of Southwest

Calling

on

Large

Retailers ($) Arizona for more than 40 years.

them,

how69often

they used?

354uses87

1,676and

1,187

3,202are 680

39 1,683 1,106

The company was founded by Mr. Terrence

St. Julian

1995

To better

understand

customers,

Mr. Selig

883 3,140

299 2,197

175 159the1,105

434 615

149 asked 11.65

1,116 681 1,294

12 754 1,206 1,448 870 90.8

944 1,255

and is run today by his son Cory. The company has

Wendy

of 2000

planning,

1,168Ms.278

579Lamberg,

7 357director

252 1,602

2,321 to 4select

392 a sam- 14.02

1,213 1,291 719 934 1,313 1,083 899 850109.2

886 1,556

grown from a handful of employees to more than 500

ple

of

customers

and

prepare

a

report.

To

begin,

she

has

416 427 1,738 526 13 1,604 249 557 635 527

886 1,315 1,858 1,262 1,338 1,066 807 1,244 758 918

today. Cory is concerned about several

positions within

125.7

appointed a team from her staff.2005

You are the head of the 16.13

the company where he has men and women doing esteam and responsible for preparing

the report. You select a 19.97

2013

155.6

sentially

the

same

job

but

at

different

pay. To investirandom sample of 60 customers. In addition to the balance

gate, he collected the information below.

Suppose you

2016

166.5

PRA

C T Iaccount

CE T

T of last

in each

at E

theSend

month, you determine 21.37

are a student intern in the Accounting Department and

(1) the number of ATM (automatic teller machine) transac2016

Average

wage

Increased

86.5%

from

the

average

of

1995,

2000

have

been

given

the

task

to

write

a

report

summarizing

Theretions

is a practice

test

at

the

end

of

each

review

section.

The

tests

are

in

two

parts.

The

first

part

contains

several

objecin the last month; (2) the number of other bank serthe

situation.In most cases, it should take 30 to 45

tive questions,

usuallyaccount,

in a fill-in-the-blank

Theetc.)

second

problems.

vices (a savings

a certificate format.

of deposit,

the part is

minutes

to complete

test. Thethe

problems

require

calculator.

Check the answers in the Answer Section in the back of

customer

uses; the

(3) whether

customer

aadebit

card

17–2

1.hasa.

P1 =

($85/$75)(100)

113.3

Yearly =

Salary

($000)

Women

Men

the book.

(this is a bank service in which charges are made directly

to

Less than

2

0

= 30

112.5

P2 = ($45/$40)(100)

the customer’s account); and (4) whether or not interest

is

Part paid

1—Objective

30 up to 40

3

1

on the checking account. The sample includes cusPAtlanta,

= (113.3

+ 112.5)/2

tomers

fromof the

branches

in Cincinnati,

Ohio;analyzing,

1. The

science

collecting,

organizing,

presenting,

and interpreting

to 112.9

assist in

40 data

up to=

50

17

4

Georgia;

Louisville,

Kentucky;

and Erie, Pennsylvania.

.

making

effective

decisions

is called

50 up to =

60 113.0 1. 17

24

b.

P = ($130/$115)(100)

2. Methods of organizing, summarizing, and presenting data in an informative60

way

are

up to 70

8

21

1. Develop a graph or table that portrays the checking

$85(500) + $45(1,200)

.

called

70 up to 80

7

balances. What is the balance of a typical

c.customer?

P=

(100)2. 3

3. The entire set of individuals or objects of interest or the measurements obtained

from all

80 or more

0

3

$75(500)

+

$40(1,200)

Do many customers have more than $2,000 in their

individuals or objects of interest are called the

.

3.

accounts? Does it appear that there is a difference in

4. List the two types of variables.

$96,500

To kick off the project, Mr. Cory4.St. Julian held a meeting

the distribution of the accounts among the four

(100)

=and112.9

5. The number of bedrooms in a house is an example of=a

. (discrete

variable,

with

his staff

you were invited. At this meeting, it was

branches? Around what value do the account bal85,500

continuous variable, qualitative variable—pick one)

5. several measures of

suggested that you calculate

ances tend to cluster?

6. The jersey numbers of Major League Baseball players are an example of what level of

measurement?

6.

7. The classification of students by eye color is an example of what level of measurement?

7.

8. The sum of the differences between each value and the mean is always equal to what value? 8.

9. A set of data contained 70 observations. How many classes would the 2k method suggest to

construct a frequency distribution?

9.

10. What percent of the values in a data set are always larger than the median?

10.

11. The square of the standard deviation is the

.

11.

xi

17

1/10/17 7:4

C

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xiv

AC KN OWLE DG M E NTS

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Central Michigan University

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Northeast Mississippi Community

College

John Beyers

University of Maryland

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University of North Carolina

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Loyola Marymount University

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El Paso Community College

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xv

xvi

CONTENTS

EN

H A N C E M E NTS TO

STATI STI CA L TE C H N I QU E S

I N BUS I N E SS & E CO N O M I C S , 17E

MAJOR CHANGES MADE TO INDIVIDUAL

CHAPTERS:

CHAPTER 1 What Is Statistics?

CHAPTER 8 Sampling Methods and the Central

Limit Theorem

• New Data Analytics section with new data and questions.

• Revised Self-Review 1-2.

CHAPTER 9 Estimation and Confidence Intervals

• New Section describing Business Analytics and its integration

with the text.

• New Self-Review 9-3 problem description.

• Updated exercises 2, 3, 17, and 19.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 2 Describing Data: Frequency Tables,

Frequency Distributions, and Graphic Presentation

• Updated exercises 5, 6, 12, 14, 23, 24, 33, 41, 43, and 61.

CHAPTER 10 One-Sample Tests

of Hypothesis

• Revised chapter introduction.

• Revised the Example/Solutions using an airport, cell phone

parking lot as the context.

• Added more explanation about cumulative relative frequency

distributions.

• Revised the section on Type II error to include an additional

example.

• Updated exercises 47 and 48 using real data.

• New Type II error exercises, 23 and 24.

• New Data Analytics section with new data and questions.

• Updated exercises 19, 31, 32, and 43.

CHAPTER 3 Describing Data:

Numerical Measures

• Updated Self-Review 3-2.

• Updated Exercises 16, 18, 73, 77, and 82.

• New Data Analytics section with new data and questions.

CHAPTER 4 Describing Data: Displaying and

Exploring Data

• New Data Analytics section with new data and questions.

CHAPTER 11 Two-Sample Tests

of Hypothesis

• Updated exercises 5, 9, 12, 26, 27, 30, 32, 34, 40, 42,

and 46.

• New Data Analytics section with new data and questions.

CHAPTER 12 Analysis of Variance

• Updated exercise 22 with 2016 New York Yankee player

salaries.

• Revised Self-Reviews 12-1 and 12-3.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 5 A Survey of Probability Concepts

CHAPTER 13 Correlation and Linear Regression

• Revised the Example/Solution in the section on Bayes

Theorem.

• Added new conceptual formula, to relate the standard error

to the regression ANOVA table.

• Updated exercises 45 and 58 using real data.

• Updated exercises 36, 41, 42, 43, and 57.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 6 Discrete Probability Distributions

CHAPTER 14 Multiple Regression Analysis

• Expanded discussion of random variables.

• Updated exercises 19, 21, 23, 24, and 25.

• Revised the Example/Solution in the section on Poisson

distribution.

• New Data Analytics section with new data and questions.

• Updated exercises 18, 58, and 68.

• New Data Analytics section with new data and questions.

CHAPTER 7 Continuous Probability Distributions

• Updated exercises 10, 21, 24, 33, 38, 42, and 44.

CHAPTER 15 Nonparametric Methods: Nominal

Level Hypothesis Tests

• Updated the context of Manelli Perfume Company Example/

Solution.

• Revised the Example/Solutions using Uber as the context.

• Revised the “Hypothesis Test of Unequal Expected Frequencies” Example/Solution.

• Updated exercises 19, 22, 28, 36, 47, and 64.

• Updated exercises 3, 31, 42, 46, and 61.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

• Revised Self-Review 7-1.

xvi

CHAPTER 16 Nonparametric Methods: Analysis of

Ordinal Data

CHAPTER 18 Time Series and Forecasting

• Revised the “Sign Test” Example/Solution.

• New Data Analytics section with new data and questions.

• Revised the “Testing a Hypothesis About a Median” Example/

Solution.

• Revised the “Wilcoxon Rank-Sum Test for Independent Populations” Example/Solution.

• Revised Self-Reviews 16-3 and 16-6.

• Updated exercise 25.

• Updated dates, illustrations, and examples.

CHAPTER 19 Statistical Process Control and

Quality Management

• Updated 2016 Malcolm Baldridge National Quality Award

winners.

• Updated exercises 13, 22, and 25.

• New Data Analytics section with new data and questions.

CHAPTER 17 Index Numbers

• Revised Self-Reviews 17-1, 17-2, 17-3, 17-4, 17-5, 17-6, 17-7.

• Updated dates, illustrations, and examples.

• New Data Analytics section with new data and questions.

xvii

BRIEF CONTENTS

1 What is Statistics? 1

2 Describing Data: Frequency Tables, Frequency Distributions,

and Graphic Presentation

18

3 Describing Data: Numerical Measures 51

4 Describing Data: Displaying and Exploring Data 94

5 A Survey of Probability Concepts 132

6 Discrete Probability Distributions 175

7 Continuous Probability Distributions 209

8 Sampling Methods and the Central Limit Theorem

9 Estimation and Confidence Intervals 282

10 One-Sample Tests of Hypothesis 318

11 Two-Sample Tests of Hypothesis 353

12 Analysis of Variance 386

13 Correlation and Linear Regression 436

14 Multiple Regression Analysis 488

15 Nonparametric Methods:

Nominal Level Hypothesis Tests

16

7

1

18

19

20

Nonparametric Methods:

Analysis of Ordinal Data

Index Numbers

Review Section

250

Review Section

Review Section

Review Section

545

582

Review Section

621

Time Series and Forecasting

653

Review Section

Statistical Process Control and Quality Management

An Introduction to Decision Theory

Glossary

Index

697

728

Appendixes:

Data Sets, Tables, Software Commands, Answers

Review Section

745

847

851

xix

CONTENTS

A Note from the Authors

vi

1What is Statistics?

1

Introduction 2

Why Study Statistics? 2

What is Meant by Statistics? 3

E X E RC ISE S 41

Chapter Summary 42

Chapter Exercises 43

Data Analytics 49

Types of Statistics 4

Descriptive Statistics 4

Inferential Statistics 5

Types of Variables 6

Levels of Measurement 7

Nominal-Level Data 7

Ordinal-Level Data 8

Interval-Level Data 9

Ratio-Level Data 10

EX ERCISES 11

Ethics and Statistics 12

Basic Business Analytics 12

3Describing Data:

NUMERICAL MEASURES

51

Introduction 52

Measures of Location 52

The Population Mean 53

The Sample Mean 54

Properties of the Arithmetic

Mean 55

E X E RC ISE S 56

Chapter Summary 13

The Median 57

The Mode 59

Chapter Exercises 14

E X E RC ISE S 61

Data Analytics 17

The Relative Positions of the Mean,

Median, and Mode 62

E X E RC ISE S 63

2Describing Data:

FREQUENCY TABLES, FREQUENCY

DISTRIBUTIONS, AND GRAPHIC

PRESENTATION 18

E X E RC ISE S 66

The Geometric Mean 66

Introduction 19

E X E RC ISE S 68

Constructing Frequency Tables 19

Why Study Dispersion? 69

Relative Class Frequencies 20

Graphic Presentation

of Qualitative Data 21

EX ERCISES 25

Constructing Frequency

Distributions 26

Relative Frequency Distribution 30

EX ERCISES 31

Graphic Presentation of a Distribution 32

Histogram 32

Frequency Polygon 35

EX ERCISES 37

Cumulative Distributions 38

xx

Software Solution 64

The Weighted Mean 65

Range 70

Variance 71

E X E RC ISE S 73

Population Variance 74

Population Standard Deviation 76

E X E RC ISE S 76

Sample Variance and Standard

Deviation 77

Software Solution 78

E X E RC ISE S 79

Interpretation and Uses of the Standard

Deviation 79

Chebyshev’s Theorem 79

The Empirical Rule 80

xxi

CONTENTS

EXER C ISES 81

E X E RC ISE S 140

The Mean and Standard Deviation

of Grouped Data 82

Rules of Addition for Computing

Probabilities 141

Arithmetic Mean of Grouped Data 82

Standard Deviation of Grouped Data 83

EXER C ISES 85

Ethics and Reporting Results 86

E X E RC ISE S 146

Chapter Summary 86

Rules of Multiplication

to Calculate Probability 147

Pronunciation Key 88

Chapter Exercises 88

Data Analytics 92

Special Rule of Multiplication 147

General Rule of Multiplication 148

Contingency Tables 150

4Describing Data:

Special Rule of Addition 141

Complement Rule 143

The General Rule of Addition 144

DISPLAYING AND EXPLORING DATA 94

Tree Diagrams 153

E X E RC ISE S 155

Bayes’ Theorem 157

Introduction 95

E X E RC ISE S 161

Dot Plots 95

Principles of Counting 161

Stem-and-Leaf Displays 96

EXER C ISES 101

Measures of Position 103

Quartiles, Deciles, and Percentiles 103

EXER C ISES 106

The Multiplication Formula 161

The Permutation Formula 163

The Combination Formula 164

E X E RC ISE S 166

Chapter Summary 167

Pronunciation Key 168

Box Plots 107

Chapter Exercises 168

EXER C ISES 109

Data Analytics 173

Skewness 110

EXER C ISES 113

Describing the Relationship between

Two Variables 114

Contingency Tables 116

6Discrete Probability

Distributions 175

Introduction 176

EXER C ISES 118

Chapter Summary 119

What is a Probability Distribution? 176

Pronunciation Key 120

Random Variables 178

Chapter Exercises 120

Data Analytics 126

Discrete Random Variable 179

Continuous Random Variable 179

The Mean, Variance, and Standard Deviation of a

Discrete Probability Distribution 180

Problems 127

Cases 129

Mean 180

Variance and Standard Deviation 180

Practice Test 130

E X E RC ISE S 182

5A Survey of Probability

Concepts 132

Introduction 133

What is a Probability? 134

Approaches to Assigning Probabilities 136

Classical Probability 136

Empirical Probability 137

Subjective Probability 139

Binomial Probability Distribution 184

How Is a Binomial Probability

Computed? 185

Binomial Probability Tables 187

E X E RC ISE S 190

Cumulative Binomial Probability

Distributions 191

E X E RC ISE S 193

Hypergeometric Probability Distribution 193

xxiiCONTENTS

EX ERCISES 197

E X E RC ISE S 257

Poisson Probability Distribution 197

Sampling “Error” 259

EX ERCISES 202

Sampling Distribution of the Sample Mean 261

Chapter Summary 202

E X E RC ISE S 264

Chapter Exercises 203

The Central Limit Theorem 265

Data Analytics 208

7Continuous Probability

Distributions 209

Introduction 210

The Family of Uniform Probability

Distributions 210

EX ERCISES 213

The Family of Normal Probability Distributions 214

The Standard Normal Probability

Distribution 217

Applications of the Standard Normal

Distribution 218

The Empirical Rule 218

EX ERCISES 220

Finding Areas under the Normal Curve 221

EX ERCISES 224

EX ERCISES 226

EX ERCISES 229

The Normal Approximation

to the Binomial 229

Continuity Correction Factor 230

How to Apply the Correction Factor 232

EX ERCISES 233

The Family of Exponential Distributions 234

EX ERCISES 238

Chapter Summary 239

Chapter Exercises 240

Data Analytics 244

Problems 246

Cases 247

Practice Test 248

8Sampling Methods and the

Central Limit Theorem 250

Introduction 251

Sampling Methods 251

Reasons to Sample 251

Simple Random Sampling 252

Systematic Random Sampling 255

Stratified Random Sampling 255

Cluster Sampling 256

E X E RC ISE S 271

Using the Sampling Distribution of the

Sample Mean 273

E X E RC ISE S 275

Chapter Summary 275

Pronunciation Key 276

Chapter Exercises 276

Data Analytics 281

9Estimation and Confidence

Intervals 282

Introduction 283

Point Estimate for a Population Mean 283

Confidence Intervals for a Population Mean 284

Population Standard Deviation, Known σ 284

A Computer Simulation 289

E X E RC ISE S 291

Population Standard Deviation, σ Unknown 292

E X E RC ISE S 299

A Confidence Interval for a Population

Proportion 300

E X E RC ISE S 303

Choosing an Appropriate Sample Size 303

Sample Size to Estimate a Population Mean 304

Sample Size to Estimate a Population

Proportion 305

E X E RC ISE S 307

Finite-Population Correction Factor 307

E X E RC ISE S 309

Chapter Summary 310

Chapter Exercises 311

Data Analytics 315

Problems 316

Cases 317

Practice Test 317

10One-Sample Tests

of Hypothesis 318

Introduction 319

What is Hypothesis Testing? 319

xxiii

CONTENTS

Six-Step Procedure for Testing

a Hypothesis 320

Step 1: State the Null Hypothesis (H0) and the

Alternate Hypothesis (H1) 320

Step 2: Select a Level of Significance 321

Step 3: Select the Test Statistic 323

Step 4: Formulate the Decision Rule 323

Step 5: Make a Decision 324

Step 6: Interpret the Result 324

One-Tailed and Two-Tailed Hypothesis Tests 325

Hypothesis Testing for a Population Mean: Known

Population Standard Deviation 327

A Two-Tailed Test 327

A One-Tailed Test 330

p-Value in Hypothesis Testing 331

Chapter Exercises 378

Data Analytics 385

12Analysis of Variance

Introduction 387

Comparing Two Population Variances 387

The F Distribution 387

Testing a Hypothesis of Equal Population

Variances 388

E X E RC ISE S 391

ANOVA: Analysis of Variance 392

ANOVA Assumptions 392

The ANOVA Test 394

EXER C ISES 333

E X E RC ISE S 401

Hypothesis Testing for a Population Mean:

Population Standard Deviation Unknown 334

Inferences about Pairs of Treatment

Means 402

EXERC ISES 339

E X E RC ISE S 404

A Statistical Software Solution 340

Two-Way Analysis of Variance 406

EXERC ISES 342

E X E RC ISE S 411

Type II Error 343

Two-Way ANOVA with Interaction 412

EXERC ISES 346

Chapter Summary 347

Pronunciation Key 348

Chapter Exercises 348

Data Analytics 352

386

Interaction Plots 412

Testing for Interaction 413

Hypothesis Tests for Interaction 415

E X E RC ISE S 417

Chapter Summary 418

Pronunciation Key 420

11Two-Sample Tests

of Hypothesis 353

Chapter Exercises 420

Data Analytics 429

Problems 431

Introduction 354

Cases 433

Two-Sample Tests of Hypothesis: Independent

Samples 354

Practice Test 434

EXERC ISES 359

Comparing Population Means with Unknown

Population Standard Deviations 360

Two-Sample Pooled Test 360

EXERC ISES 364

Unequal Population Standard

Deviations 366

EXERC ISES 369

Two-Sample Tests of Hypothesis:

Dependent Samples 370

Comparing Dependent

and Independent Samples 373

EXERC ISES 375

13Correlation and

Linear Regression

436

Introduction 437

What is Correlation Analysis? 437

The Correlation Coefficient 440

E X E RC ISE S 445

Testing the Significance of the Correlation

Coefficient 447

E X E RC ISE S 450

Regression Analysis 451

Least Squares Principle 451

Drawing the Regression Line 454

Chapter Summary 377

E X E RC ISE S 457

Pronunciation Key 378

Testing the Significance of the Slope 459

xxivCONTENTS

EX ERCISES 461

Qualitative Independent Variables 512

Evaluating a Regression Equation’s

Ability to Predict 462

Regression Models with Interaction 515

Stepwise Regression 517

The Standard Error of Estimate 462

The Coefficient of Determination 463

E X E RC ISE S 519

Review of Multiple Regression 521

EX ERCISES 464

Chapter Summary 527

Relationships among the Correlation

Coefficient, the Coefficient of

Determination, and the Standard

Error of Estimate 464

Pronunciation Key 528

Chapter Exercises 529

Data Analytics 539

EX ERCISES 466

Problems 541

Interval Estimates of Prediction 467

Cases 542

Assumptions Underlying Linear

Regression 467

Constructing Confidence and Prediction

Intervals 468

EX ERCISES 471

Transforming Data 471

Practice Test 543

15Nonparametric Methods:

NOMINAL LEVEL HYPOTHESIS TESTS 545

EX ERCISES 474

Introduction 546

Chapter Summary 475

Pronunciation Key 477

Test a Hypothesis of a Population

Proportion 546

Chapter Exercises 477

E X E RC ISE S 549

Data Analytics 487

Two-Sample Tests about Proportions 550

E X E RC ISE S 554

14Multiple Regression

Analysis 488

Goodness-of-Fit Tests: Comparing Observed and

Expected Frequency Distributions 555

Hypothesis Test of Equal Expected

Frequencies 555

Introduction 489

E X E RC ISE S 560

Multiple Regression Analysis 489

Hypothesis Test of Unequal Expected

Frequencies 562

EX ERCISES 493

Evaluating a Multiple Regression Equation 495

Limitations of Chi-Square 563

The ANOVA Table 495

Multiple Standard Error of Estimate 496

Coefficient of Multiple Determination 497

Adjusted Coefficient of Determination 498

E X E RC ISE S 565

Testing the Hypothesis That a Distribution is

Normal 566

EX ERCISES 499

E X E RC ISE S 569

Inferences in Multiple Linear

Regression 499

Contingency Table Analysis 570

E X E RC ISE S 573

Global Test: Testing the Multiple

Regression Model 500

Evaluating Individual Regression

Coefficients 502

Chapter Summary 574

Pronunciation Key 575

Chapter Exercises 576

EX ERCISES 505

Data Analytics 581

Evaluating the Assumptions of Multiple

Regression 506

Linear Relationship 507

Variation in Residuals Same for Large

and Small ŷ Values 508

Distribution of Residuals 509

Multicollinearity 509

Independent Observations 511

16Nonparametric Methods:

ANALYSIS OF ORDINAL DATA 582

Introduction 583

The Sign Test 583

Techniques

in Business

& Economics

Seventeenth Edition

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MARCHAL

WATHEN

Statistical Techniques in

BUSINESS &

ECONOMICS

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Statistical Techniques in

BUSINESS &

ECONOMICS

SEVENTEENTH EDITION

DOUGLAS A. LIND

Coastal Carolina University and The University of Toledo

WILLIAM G. MARCHAL

The University of Toledo

SAMUEL A. WATHEN

Coastal Carolina University

STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS, SEVENTEENTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by

McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions

© 2015, 2012, and 2010. No part of this publication may be reproduced or distributed in any form or

by any means, or stored in a database or retrieval system, without the prior written consent of McGrawHill Education, including, but not limited to, in any network or other electronic storage or transmission,

or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside

the United States.

This book is printed on acid-free paper.

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All credits appearing on page or at the end of the book are considered to be an extension of the

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Library of Congress Cataloging-in-Publication Data

Names: Lind, Douglas A., author. | Marchal, William G., author. | Wathen,

Samuel Adam. author.

Title: Statistical techniques in business & economics/Douglas A. Lind,

Coastal Carolina University and The University of Toledo, William G.

Marchal, The University of Toledo, Samuel A. Wathen, Coastal Carolina University.

Other titles: Statistical techniques in business and economics

Description: Seventeenth Edition. | Dubuque, IA : McGraw-Hill Education,

[2017] | Revised edition of the authors’ Statistical techniques in

business & economics, [2015]

Identifiers: LCCN 2016054310| ISBN 9781259666360 (alk. paper) | ISBN

1259666360 (alk. paper)

Subjects: LCSH: Social sciences—Statistical methods. |

Economics—Statistical methods. | Commercial statistics.

Classification: LCC HA29 .M268 2017 | DDC 519.5—dc23 LC record available at

https://lccn.loc.gov/2016054310

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a

website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill

Education does not guarantee the accuracy of the information presented at these sites.

mheducation.com/highered

D E D I CATI O N

To Jane, my wife and best friend, and our sons, their wives, and our

grandchildren: Mike and Sue (Steve and Courtney), Steve and Kathryn

(Kennedy, Jake, and Brady), and Mark and Sarah (Jared, Drew, and Nate).

Douglas A. Lind

To Oscar Sambath Marchal, Julian Irving Horowitz, Cecilia Marchal

Nicholson and Andrea.

William G. Marchal

To my wonderful family: Barb, Hannah, and Isaac.

Samuel A. Wathen

A

NOTE

FROM

THE

AUTHOR

S

Over the years, we received many compliments on this text and understand that it’s a

favorite among students. We accept that as the highest compliment and continue to

work very hard to maintain that status.

The objective of Statistical Techniques in Business and Economics is to provide

students majoring in management, marketing, finance, accounting, economics, and

other fields of business administration with an introductory survey of descriptive and inferential statistics. To illustrate the application of statistics, we use many examples and

exercises that focus on business applications, but also relate to the current world of the

college student. A previous course in statistics is not necessary, and the mathematical

requirement is first-year algebra.

In this text, we show beginning students every step needed to be successful in

a basic statistics course. This step-by-step approach enhances performance, accelerates preparedness, and significantly improves motivation. Understanding the

concepts, seeing and doing plenty of examples and exercises, and comprehending

the application of statistical methods in business and economics are the focus of

this book.

The first edition of this text was published in 1967. At that time, locating relevant

business data was difficult. That has changed! Today, locating data is not a problem.

The number of items you purchase at the grocery store is automatically recorded at

the checkout counter. Phone companies track the time of our calls, the length of calls,

and the identity of the person called. Credit card companies maintain information on

the number, time and date, and amount of our purchases. Medical devices automatically monitor our heart rate, blood pressure, and temperature from remote locations.

A large amount of business information is recorded and reported almost instantly.

CNN, USA Today, and MSNBC, for example, all have websites that track stock prices

in real time.

Today, the practice of data analytics is widely applied to “big data.” The practice

of data analytics requires skills and knowledge in several areas. Computer skills are

needed to process large volumes of information. Analytical skills are needed to

evaluate, summarize, organize, and analyze the information. Critical thinking skills

are needed to interpret and communicate the results of processing the

information.

Our text supports the development of basic data analytical skills. In this edition,

we added a new section at the end of each chapter called Data Analytics. As you

work through the text, this section provides the instructor and student with opportunities to apply statistical knowledge and statistical software to explore several business environments. Interpretation of the analytical results is an integral part of these

exercises.

A variety of statistical software is available to complement our text. Microsoft Excel

includes an add-in with many statistical analyses. Megastat is an add-in available for

Microsoft Excel. Minitab and JMP are stand-alone statistical software available to download for either PC or MAC computers. In our text, Microsoft Excel, Minitab, and Megastat

are used to illustrate statistical software analyses. When a software application is presented, the software commands for the application are available in Appendix C. We use

screen captures within the chapters, so the student becomes familiar with the nature of

the software output.

Because of the availability of computers and software, it is no longer necessary to

dwell on calculations. We have replaced many of the calculation examples with interpretative ones, to assist the student in understanding and interpreting the statistical results.

In addition, we place more emphasis on the conceptual nature of the statistical topics.

While making these changes, we still continue to present, as best we can, the key concepts, along with supporting interesting and relevant examples.

vi

WHAT’S NEW IN THE SEVENTEENTH EDITION?

We have made many changes to examples and exercises throughout the text. The section on “Enhancements” to our text details them. The major change to the text is in

response to user interest in the area of data analytics. Our approach is to provide instructors and students with the opportunity to combine statistical knowledge, computer

and statistical software skills, and interpretative and critical thinking skills. A set of new

and revised exercises is included at the end of chapters 1 through 18 in a section titled

“Data Analytics.”

In these sections, exercises refer to three data sets. The North Valley Real Estate

sales data set lists 105 homes currently on the market. The Lincolnville School District

bus data lists information on 80 buses in the school district’s bus fleet. The authors designed these data so that students will be able to use statistical software to explore the

data and find realistic relationships in the variables. The Baseball Statistics for the 2016

season is updated from the previous edition.

The intent of the exercises is to provide the basis of a continuing case analysis. We

suggest that instructors select one of the data sets and assign the corresponding exercises as each chapter is completed. Instructor feedback regarding student performance

is important. Students should retain a copy of each chapter’s results and interpretations

to develop a portfolio of discoveries and findings. These will be helpful as students

progress through the course and use new statistical techniques to further explore the

data. The ideal ending for these continuing data analytics exercises is a comprehensive

report based on the analytical findings.

We know that working with a statistics class to develop a very basic competence in

data analytics is challenging. Instructors will be teaching statistics. In addition, instructors will be faced with choosing statistical software and supporting students in developing or enhancing their computer skills. Finally, instructors will need to assess student

performance based on assignments that include both statistical and written components. Using a mentoring approach may be helpful.

We hope that you and your students find this new feature interesting and engaging.

vii

H OW A R E C H A P TE RS O RGA N I Z E D TO E N GAG E

DESCRIBING

DATA:

STU D E NTS A N D PRO M OTE

LE

ADISPLAYING

RN I NAND

G?EXPLORING DATA

95

INTRODUCTION

Chapter 2 began our study of descriptive statistics. In order to transform raw or ungrouped data into a meaningful form, we organize the data into a frequency distribution.

We present the frequency distribution in graphic form as a histogram or a frequency

polygon.

This

allowsrecently

us to visualize

data tend

to cluster,

the for

largest

and the

MERRILL

LYNCH

completedwhere

a studythe

of online

investment

portfolios

a sample

Each chapter begins with a set of

smallest

values,

and

general in

shape

of the

data. these data into a frequency

of clients.

For the

70the

participants

the study,

organize

)

distribution.

(See

and LO2-3.

In Chapter

3, Exercise

we first 43

computed

several

measures of location, such as the mean,

learning objectives designed to promedian, and mode. These measures of location allow us to report a typical value in the

vide focus for the chapter and motivate

set of observations. We also computed several measures of dispersion, such as the

student learning. These objectives, lorange, variance, and standard deviation. These measures of dispersion allow us to deLEARNING OBJECTIVES

cated in the margins next to the topic,

scribe the variation or the spread in a set of observations.

When you have completed this chapter, you will be able to:

We continue our study of descriptive statistics in this chapter. We study (1) dot plots,

indicate what the student should be

Summarize

qualitative(3)

variables

with frequency

tables. and statistics

(2)LO2-1

stem-and-leaf

displays,

percentiles,

and (4)and

boxrelative

plots.frequency

These charts

able to do after completing each secgive

us additional

insight into

are concentrated as well as the general

LO2-2

Display a frequency

tablewhere

using athe

bar values

or pie chart.

tion in the chapter.

shape of the data. Then we consider bivariate data. In bivariate data, we observe two

LO2-3 Summarize quantitative variables with frequency and relative frequency distributions.

variables for each individual or observation. Examples include the number of hours a

LO2-4 studied

Display aand

frequency

distribution

using

or frequency

student

the points

earned

ona histogram

an examination;

if a polygon.

sampled product meets

quality specifications and the shift on which it is manufactured; or the amount of electricity used in a month by a homeowner and the mean daily high temperature in the region

theshows

month. how

These the

charts

and graphs

provide

useful

as to

weause

business

A representative exercise opens the chapter for

and

chapter

content

can

be insights

applied

real-world

analytics to enhance our understanding of data.

situation.

Chapter Learning Objectives

Source: © rido/123RF

Chapter Opening Exercise

19

DESCRIBING DATA: FREQUENCY TABLES, FREQUENCY DISTRIBUTIONS, AND GRAPHIC PRESENTATION

LO4-1

Construct and interpret a

dot plot.

Introduction to the Topic

DOT PLOTS

INTRODUCTION

Recall for the Applewood

Auto Group data, we summarized the profit earned on the

The

United

States automobile

retailing industry

highlyclasses.

competitive.

It is dominated

by

180 vehicles sold

with

a frequency

distribution

using iseight

When

we orgamegadealerships

that ownwe

andlost

operate

or more

franchises,

over 10,000

Each chapter starts with a review of

nized the data into

the eight classes,

the 50

exact

value

of the employ

observations.

A

people, and generate several billion dollars in annual sales. Many of the top dealerships

dot plot, on the other hand, groups

theowned

datawith

as shares

little as

possible,

andYork

weStock

do not

lose

the important concepts of the previare publicly

traded

on the New

Exchange

the identity

of an individual observation.

To develop

dot plot, we was

display

a dot(ticker

for

Lin66360_ch02_018-050.indd

18

or NASDAQ. In 2014,

the largestamegadealership

AutoNation

ous chapter and provides a link to the

symbol AN),

followedline

by Penske

Auto Group

(PAG), Group

1 Automotive,

each observation along a horizontal

number

indicating

the possible

values

of the

Inc. (ticker symbol

GPI),

and the privately

Van Tuyl

material in the current chapter. This

data. If there are identical observations

or the

observations

areowned

too close

toGroup.

be shown

These large corporations use statistics and analytics to summarize

individually, the dots are “piled”

on

top

of

each

other.

This

allows

us

to

see

theAsshape

step-by-step approach increases comand analyze data and information to support their decisions.

an exof the distribution, the value about

which

the at

data

tend to cluster,

and Itthe

largest

and

ample, we

will look

the Applewood

Auto group.

owns

four dealerprehension by providing continuity

shipsare

andmost

sells auseful

wide range

of vehicles.

the popular

smallest observations. Dot plots

for smaller

dataThese

sets,include

whereas

histoacross the concepts.

brands

Kia sets.

and Hyundai,

BMW and

sedans

luxury

grams tend to be most usefulKorean

for large

data

An example

willVolvo

show

howand

to conand a full line of Ford and Chevrolet cars and trucks.

struct and interpret dot plots.SUVs,

Ms. Kathryn Ball is a member of the senior management team at

Applewood Auto Group, which has its corporate offices adjacent to Kane

Motors. She is responsible for tracking and analyzing vehicle sales and

the profitability of those vehicles. Kathryn would like to summarize the profit earned on

the vehicles sold with tables, charts, and graphs that she would review monthly. She

E X A M P L E wants to know the profit per vehicle sold, as well as the lowest and highest amount of

profit. She is also interested in describing the demographics of the buyers. What are

The service departments

at many

Tionesta

Ford

and Sheffield

their ages? How

vehicles

haveLincoln

they previously

purchasedMotors

from oneInc.,

of thetwo

Appleof the four Applewood

Auto Group

were

both open 24 days last

wood dealerships?

What typedealerships,

of vehicle did they

purchase?

The Applewood

Auto Group

operates four

dealerships:

month. Listed below

is the number

of vehicles

serviced

last month at the two

Source: © Justin Sullivan/Getty Images

Example/Solution

After important concepts are introduced,

a solved example is given. This example

provides a how-to illustration and shows

a relevant business application that

helps students answer the question,

“How can I apply this concept?”

dealerships. Construct

dot

plots

andsells

report

summary

statistics

to compare the

• Tionesta

Ford

Lincoln

Ford and

Lincoln cars

and trucks.

• Olean Automotive Inc. has the Nissan franchise as well as the General Motors

two dealerships.

brands of Chevrolet, Cadillac, and GMC Trucks.

• Sheffield Motors Inc. sells Buick, GMC trucks, Hyundai, and Kia.

• Kane Motors offers

the Chrysler,

Dodge, and Jeep line as well as BMW and Volvo.

Tionesta

Ford Lincoln

Monday

month, Ms. Ball

collects data

from each

of the four dealerships

Tuesday Every

Wednesday

Thursday

Friday

Saturday

and enters them into an Excel spreadsheet. Last month the Applewood

23

30

CHAPTER294

106

33Auto Group27

28 at the 39

26

sold 180 vehicles

four dealerships.

A copy of the first

32few observations

28 appears 33

35 variables

32collected include:

to the left. The

25 • Age—the

36 age of the buyer

31 at the 32

27

time of the purchase.

32 • Profit—the

35 amount earned

37

36 dealership

30 on the sale of each

by the

35

vehicle.

calculate quartiles. Excel

and Excel

2016 offer

both

The

Excel function,

• 2013

Location—the

dealership

where

themethods.

vehicle was

purchased.

Quartile.exc, will result

the same

answer sedan,

as Equation

4–1.

The or

Excel

function, Quar •in Vehicle

type—SUV,

compact,

hybrid,

truck.

•Excel

tile.inc, will result in the

Method answers.

Previous—the

number of vehicles previously purchased at any of the

Self-Reviews

Self-Reviews are interspersed

throughout each chapter and

follow Example/Solution sections. They help

students monLin66360_ch04_094-131.indd

95

itor their progress and provide

immediate reinforcement for

that particular technique. Answers are in Appendix E.

four Applewood dealerships by the consumer.

SELF-REVIEW

The entire data set is available at the McGraw-Hill website (www.mhhe

.com/lind17e) and in Appendix A.4 at the end of the text.

4–2

The Quality Control department of Plainsville Peanut Company is responsible for checking

CONSTRUCTING FREQUENCY TABLES

LO2-1

the weight of the 8-ounce jar of peanut butter. The weights of a sample of nine jars proSummarize qualitative

duced last hour are:

Recall from Chapter 1 that techniques used to describe a set of data are called descrip1/10/17 7:41 PM

variables with frequency

tive statistics. Descriptive statistics organize data to show the general pattern of the

and relative frequency

7.72where

7.8values

7.86tend 7.90

7.94

7.97

8.06

8.09

data, 7.69

to identify

to concentrate,

and to expose

extreme or unusual

tables.

data values. The first technique we discuss is a frequency table.

(a) What is the median weight?

(b) Determine

the weights

corresponding

first anddata

thirdinto

quartiles.

FREQUENCY

TABLE

A groupingtoofthe

qualitative

mutually exclusive and

collectively exhaustive classes showing the number of observations in each class.

EXERCISES

11.

viii

Determine the median and the first and third quartiles in the following data.

46

Lin66360_ch02_018-050.indd 19

12.

47

49

49

51

53

54

54

55

55

59

Determine the median and the first and third quartiles in the following data.

1/6/17 4:52 AM

1/6/17 4:52 AM

(c)

Are the events in part (a)(i) complementary or mutually ex

The probability of passing both is .50. What is the probability of passing at least one?

21. The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green

The General Rule of Addition

swordtails (44 female and 36 male) and 60 are orange swordtails (36 female and

24 males). A fish is randomly captured from the aquarium:

a. What is the probability the selected

fish is a green

may not be mutually exclu

The outcomes

of answordtail?

experiment

b. What is the probability the selected

is male? selected a sample of 200 tourists wh

Tourist fish

Commission

c. What is the probability the selected

fishsurvey

is a male

green swordtail?

year. The

revealed

that 120 tourists went to Disney

d. What is the probability the selected fish is either a male or a green swordtail?

Gardens near Tampa. What is the probability that a person

22. A National Park Service survey of visitors to the Rocky Mountain region revealed

or Busch

Gardens?

If the

that 50% visit Yellowstone Park,World

40% visit

the Tetons,

and 35%

visitspecial

both. rule of addition is use

a touristwill

who

to Disney

Worldattractions?

is .60, found by 120/200

a. What is the probability a vacationer

visitwent

at least

one of these

tourist going to Busch Gardens is .50. The sum of these p

b. What is the probability .35 called?

however,

that this probability cannot be greater than 1. The

c. Are the events mutually exclusive?

Explain.

Statistics in Action

STATISTICS IN ACTION

ists visited both attractions and are being counted twice! A c

revealed that 60 out of 200 sampled did, in fact, visit both a

that you believe that at

bility of visiting both. Thus:

A SURVEY OF PROBABILITY CONCEPTS

145

LO5-4

To answer our question, “What is the probability a se

If you wish to get some

Calculate probabilities

Disney

World

or

Busch

Gardens?”

(1)

add

the

probability

attention at the next gathStatistics in Action articles are

usingscattered

the rules of throughWorld and the probability he or she visited Busch Garden

ering

you

attend,

announce

multiplication.

out the text, usually about two per chapter. They

In this section, we discuss the rules for computing the likelihood that two events both

RULES OF MULTIPLICATION

TO CALCULATE PROBABILITY

happen, or their joint probability.

example, 16%

of the

2016 tax returns were preprovide unique, interesting applications and hisP(Disney)For

= .60

P(Busch)

= .50

least two people present

P(Disney

Busch) What

= P(Disney)

+ P(Busch) − P(bo

pared by H&R Block and 75% of those returns

showedor

a refund.

is the likelihood

torical insights in the field of statistics.

weretax

born

on the

same

a person’s

form

was

prepared by H&R Block and the person received a refund?

= .60 + .50 − .30 = .80

64

Definitions

Definitions of new terms or terms unique to

the study of statistics are set apart from the

text and highlighted for easy reference and

review. They also appear in the Glossary at

the end of the book.

Formulas

Formulas that are used for the first time are

boxed and numbered for reference. In addition, a formula card is bound into the back of

the text that lists all the key formulas.

Exercises

date—thatillustrate

is, the same

Venn diagrams

this as the intersection of two events. To find the likelihood of

day of

the year butwe

notuse the rules of

When

two events

both

the probability

two events

happening,

multiplication.

There

areoccur,

two rules

of multipli- is called

necessarily

same

ability

cation: the

specialthe

rule

andyear.

the general

rule.(.30) that a tourist visits both attractions is an examp

If there are 30 people in

the room,

the of

probability

of

Special

Rule

Multiplication

a duplicate is .706. If there

The special

rule

of

multiplication

are

60 people3in the room, requires that two events A and B are independent.

CHAPTER

P(Disney

and Busch)

= .30

Two events

are independent

if the

occurrence

of one

event does not alter the probabilthe probability

is .994 that

ity of theatoccurrence

of the

least two people

shareother

the event.

same birthday. With as few

INDEPENDENCE

The

one of

event

has nounemployment

effect on therates?

probability of

a. What

isoccurrence

the arithmeticofmean

the Alaska

as 23 people

the

chances

JOINT

PROBABILITY

probability

that measures the likelihood two or more

the

occurrence

of

another

event.

Find

theAthat

median

are even,b.that

is .50,

at and the mode for the unemployment rates.

events will happen

concurrently.

Compute

least two c.people

sharethe

thearithmetic mean and median for just the winter (Dec–Mar) months.

Is it much different?

birthday.

Hint:

To

Onesame

way

to

think

about

independence

to assume

events A

and Bfor

occur

22.

Big Orange Trucking is is

designing

an that

information

system

use at

in differ“in-cab”

ent times.

For

example,

when

event

B occurs

after

event

A

occurs,

does

A have any

this, find

the

communications.

It must

summarize

data

from

eight sites

a region

So compute

the

general

rule

of addition,

which

is used

to

compute

thethroughout

probability

ofeffect

twoto

on

the likelihood

that

event

Bexclusive,

occurs?

Ifis:

the

answer

no, then measure

A and B of

are

independent

typical

conditions.

Compute

an is

appropriate

central

location for

probability

everyone

was

events

that

are describe

not

mutually

the

variables

wind

direction,

temperature,

and

pavement.

events. To

illustrate

independence,

The outcome of a coin

born

on a different

day and suppose two coins are©tossed.

Rostislav Glinsky/Shutterstock.com

toss (head

tail)

is unaffected

useorthe

complement

rule.by the outcome of any other prior coin toss (head or tail).

City

Wind

Direction

Temperature

Pavement

For Try

twothis

independent

events A and B,The

the probability

that A and B shows

will both

occur

is that are n

Venn

events

in your

class.

GENERAL

RULE

OF

ADDITION

P(A or following

B) = P(A) +

P(B)diagram

− P(A and B) two[5–4]

West

89the

found by multiplying Anniston,

the twoALprobabilities.

This

is thetospecial

rule

ofjoint

multiplication

events

overlap

illustrate

eventDry

that and

some people h

Atlanta,

Northwest

86

Wet

is written symbolically

as: GA

Augusta, GA

Southwest

92

Wet

For the expression

P(A or AL

B), the wordSouth

or suggests that A may

Birmingham,

91 occur or B may

Dry occur.

This

also includes

the

possibility

that A and

B may

This

use of or is sometimes

SPECIAL

RULE OF

MULTIPLICATION

P(Aoccur.

and B)

=92

P(A)P(B)

Jackson,

MS

Southwest

Dry[5–5]

called an inclusive. You

could

or B or both) to emphasize

that theTrace

union of

Meridian,

MS also write P(A

South

92

the events includes the

intersection

of A and

B.

Monroe,

LA

Southwest

93

Wet

If we compare the

general

rules of addition, the

is

Tuscaloosa,

AL and special

Southwest

93 important difference

Trace

determining if the events are mutually exclusive. If the events are mutually exclusive, then

the joint

probability DATA:

P(A and

B) is 0 andMEASURES

we could use the special rule of addition. OtherDESCRIBING

NUMERICAL

79

wise, we must account for the joint probability and use the general rule of addition.

Software Solution

Lin66360_ch05_132-174.indd 144

Exercises are included

after sec-147 E X E R C I S E SE X A M P L E

Lin66360_ch05_132-174.indd

1/10/17 7:41 PM

47–52, do the following:

What isFor

theExercises

probability

that a card chosen at random from a standard deck of cards

tions within the chapter and at

E

X

A

M

P

L

E

a. Compute

sample variance.

will be either

a king orthe

a heart?

the end of the chapter. Section

b. Determine the sample standard deviation.

Table 2–4 on page 26 shows the profit on the sales of 180 vehicles at Applewood

47.

Consider

these

values

a sample: 7, 2, 6, 2, and 3.

exercises cover the material studAuto Group. Determine the mean and the median selling price.

48.

SOLU

T IThe

O Nfollowing five values are a sample: 11, 6, 10, 6, and 7.

ied in the section. Many exercises

49.

Dave’s Automatic Door, referred to in Exercise 37, installs automatic garage

openers.

on a sample,

times, in minutes,

required

We may bedoor

inclined

to addBased

the probability

of afollowing

king andare

thethe

probability

of a heart.

But thisto

have data files available to import

S

O

L

U

T IIfdoor

Owe

N openers:

install 10

28, 32,

44, 40,

54, 38, 32,

and

creates a problem.

do that, the

king24,

of 46,

hearts

is counted

with

the42.

kings and also

into statistical software. They are

Theifsample

of eight

companies

in the aerospace

industry,

to in

with the50.

hearts.

So,

we

simply

addmodal

the probability

king (there

are 4referred

in aindeck

ofExer52

The mean,

median,

and

amountsofofa profit

are reported

the following

cise

38, was of

surveyed

as

to their

return

on

investment

last year.

The results

are

indicated with the FILE icon.

cards) to the

probability

a heart

(there

are shot).

13 in a(Reminder:

deck

of 52The

cards)

and report

17

output

(highlighted

in the

screen

instructions

tothat

create

the

10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.

out

of

52

cards

meet

the

requirement,

we

have

counted

the

king

of

hearts

twice.

We

output

appear

in

the

Software

Commands

in

Appendix

C.)

There

are

180

vehicles

Answers to the odd-numbered

51.

The Houston, Texas, Motel Owner Association conducted a survey regarding

need to subtract

1 card

17

theListed

king below

ofbehearts

is counted

once.

inweekday

the study,

sofrom

using

aincalculator

would

tedious

and prone

tobusiness-class

error. Thus,

motel

ratesthe

the so

area.

is the

room

rateonly

for

exercises are in Appendix D.

there are 16 cards that are either hearts or kings. So the probability is 16/52 = .3077.

We can use a statistical software package to find many measures of location.

guests for a sample of 10 motels.

Card

$101

$97

$103

$110

Probability

$78

$87

$101

$80

Explanation

$106

$88

A consumer

organization is

concerned

credit card debt. A

P(A)watchdog

= 4/52

4 kings

in a deckabout

of 52 cards

survey of 10 young

debt

of more

than

$2,000

Heart

P(B) adults=with

13/52credit card13

hearts

in a deck

of 52

cards showed they

paid

an averageP(A

of and

justB)over

$100 per month

balances.

Listed below

King

of Hearts

= 1/52

1 king ofagainst

hearts intheir

a deck

of 52 cards

are the amounts each young adult paid last month.

52.King

Computer Output

$110

$126

$103

$93

$99

$113

$87

The text includes many software examples, using

Excel, MegaStat®, and Minitab. The software results are

LO3-5 for a particular

illustrated in the chapters. Instructions

INTERPRETATION AND USES

software example are in AppendixExplain

C. and apply

Chebyshev’s theorem

OF THE STANDARD DEVIATION

and the Empirical Rule.

Lin66360_ch05_132-174.indd 145

STATISTICS IN ACTION

Most colleges report the

“average class size.” This

information can be mislead-

$101

$109

$100

The standard deviation is commonly used as a measure to compare the spread in two

or more sets of observations. For example, the standard deviation of the biweekly

amounts invested in the Dupree Paint Company profit-sharing plan is computed1/10/17

to be 7:41 PM

$7.51. Suppose these employees are located in Georgia. If the standard deviation for a

group of employees in Texas is $10.47, and the means are about the same, it indicates

that the amounts invested by the Georgia employees are not dispersed as much as

those in Texas (because $7.51 < $10.47). Since the amounts invested by the Georgia

employees are clustered more closely about the mean, the mean for the Georgia emix

ployees is a more reliable measure than the mean for the Texas group.

Chebyshev’s Theorem

We have stressed that a small standard deviation for a set of values indicates that these

she estimates that the probability is .025 that an applicant will not be able to repay

his or her installment loan. Last month she made 40 loans.

a. What is the probability that three loans will be defaulted?

b. What is the probability that at least three loans will be defaulted?

34. Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per

minute. The distribution of arrivals approximates a Poisson distribution.

a. What is the probability that no automobiles arrive in a particular minute?

b. What is the probability that at least one automobile arrives during a particular

minute?

35. It is estimated that 0.5% of the callers to the Customer Service department of Dell

Inc. will receive a busy signal. What is the probability that of today’s 1,200 callers at

least 5 received a busy signal?

36. In the past, schools in Los Angeles County have closed an average of 3 days each

year for weather emergencies. What is the probability that schools in Los Angeles

County will close for 4 days next year?

H OW DO E S TH I S TE X T R E I N FO RC E

STU D E NT LE A R N I N G?

BY C H A P TE R

CHAPTER SUMMARY

348

I. A random

CHAPTER

10variable is a numerical value determined by the outcome of an experiment.

244

168

1. The probability of making a Type

error is equal to the level of significance. (6–1)

μ =I Σ[xP(x)]

CHAPTER

7 probability is designated by the Greek letter α.

2. This

B. The

variance is equal to:

CHAPTER

5 II error occurs when a false null hypothesis is not rejected.

B. A Type

= Σ[(x

− μ)2isP(x)]

1. The probability of making aσ2Type

II error

designated by the Greek letter β. (6–2)

II. A probability distribution is a listing of all possible outcomes of an experiment and the

probability associated with each outcome.

A. A

discrete

distribution

assume only

The

majorprobability

characteristics

of the can

t distribution

are:certain values. The main features are:

1.

of the probabilities

1. The

It is asum

continuous

distribution.is 1.00.

2.

The

probability

of

a

particular

outcome

is

between

0.00 and 1.00.

2. It is mound-shaped and symmetrical.

3.

outcomes

are mutually

exclusive.

3. The

It is flatter,

or more

spread out,

than the standard normal distribution.

B. A

continuous

distribution

can

assume

an

infinite

number

of valuesofwithin

a specific

range.

4. There is a family of t distributions, depending on the number

degrees

of freedom.

III.

mean

and types

variance

of a probability

distribution

V. The

There

are two

of errors

that can occur

in a testare

of computed

hypothesis.as follows.

A.

mean

is equal

to:when a true null hypothesis is rejected.

A. The

A Type

I error

occurs

Chapter Summary

Each chapter contains a brief summary

of the chapter material, including vocabulary, definitions, and critical formulas.

Pronunciation Key

This section lists the mathematical symbol,

its meaning, and how to pronounce it. We

believe this will help the student retain the

meaning of the symbol and generally enhance course communications.

Chapter Exercises

2. The likelihood

of a Type

II errorthe

must

be calculated

comparing

thelimits

hypothesized

68. In establishing

warranties

on HDTVs,

manufacturer

wants

to set the

so that few

distribution to an alternate distribution based on sample results.

need repair at the manufacturer’s expense. On the other hand, the warranty period

P R O N U N C I A T I O Nwill

K

EY

must be long enough to make the purchase attractive to the buyer. For a new HDTV, the

mean number of MEANING

months until repairs are needed is 36.84 with a standard

deviation of

SYMBOL

PRONUNCIATION

P R O N U N C I A T I O N3.34Kmonths.

E Y Where should the warranty limits be set so that only 10% of the HDTVs

Lin66360_ch06_175-208.indd 202

CHAPTER

CHAPTER

Generally, the end-of-chapter exercises

are the most challenging and integrate

the chapter concepts. The answers and

worked-out solutions for all oddnumbered exercises are in Appendix D

at the end of the text. Many exercises

are noted with a data file icon in the

margin. For these exercises, there are

data files in Excel format located on the

text’s website, www.mhhe.com/Lind17e.

These files help students use statistical

software to solve the exercises.

Data Analytics

The goal of the Data Analytics sections is to develop analytical skills.

The exercises present a real world

context with supporting data. The data

sets are printed in Appendix A and

available to download from the text’s

website www.mhhe.com/Lind17e. Statistical

software is required to analyze the data

and respond to the exercises. Each data

set is used to explore questions and discover findings that relate to a real world

context. For each business context, a

story is uncovered as students progress

from chapters one to seventeen.

x

DATA ANA

P(A)

Probability of A

P of A

need repairs at the manufacturer’s expense?

SYMBOL

MEANING

P(∼A)

Probability

not A

P of not Aselects

69.

DeKorte Tele-Marketing

Inc. of

is considering

purchasing a machine thatPRONUNCIATION

randomly

H0 and

hypothesis

and B)

automaticallyProbability

dialsNull

telephone

numbers.

DeKorte Tele-MarketingHmakes

P(A

of A and

B

Psub

of zero

Amost

and Bof its

calls

so of

calls

toBbusiness phones are wasted. The

manufacturer

of

H1 or

Alternate

H Psub

P(A

B) during the evening,

Probability

Ahypothesis

or

of one

A or B

the machine claims that its programming reduces the calling to business phones to 15%

α/2| B)

Two-tailed

significance

level

Alpha

divided

P(A

Probability

of the

A given

B has

P of A

given by

Bthe2

of all calls. To test

this claim,

director

ofhappened

purchasing at DeKorte programmed

xP

Limit of of

then sample

mean r at a time

x bar

Permutation

items selected

Pnr sub c

n cr machine to select a sample of 150 phone numbers. What is the likelihood that more

numbersofselected

aremean

thoser of

assuming

the manuAssumed

population

muCnr

sub zero

μC than 30 of the phone

Combination

n items selected

at abusinesses,

time

n 0r

facturer’s claim is correct?

70. A carbon monoxide detector in the Wheelock household activates once every 200 days

average.

E X E R ConI S

E S Assume this activation follows the exponential distribution. What is the

E X E R Cprobability

I S E S that:

There will

alarm

within

the nextthe

60 mean

days? gross income of plumbers in the Salt

25. a.

According

tobe

theanlocal

union

president,

47. b.

The

department

atthe

Pepsico

plans to survey

about a newly

Atmarketing

least

400research

days will

pass

before

nextdistribution

alarm?

Lake

City area

follows

the

normal

probability

with ateenagers

mean of $45,000

and a

developed

soft

drink.

Each

will250

be

asked

to compare

with his for

or her

favorite

soft drink.

c.

It will be

between

and

days until

the nextitwarning?

standard

deviation

of150

$3,000.

A recent

investigative

reporter

KYAK

TV found,

for a

a.

What

is

the

experiment?

d.

Find the

median

time until

next

activation.

sample

of 120

plumbers,

thethe

mean

gross

income was $45,500. At the .10 significance

b.

What

one

event?thethat

71. “Boot

time”

(thepossible

time between

appearance

the Bios

screen

toto

the

first file that

is

level,

is itisreasonable

to conclude

the meanofincome

is not

equal

$45,000?

Deter48. loaded

The

of timesona Eric

particular

event

occurred

in the past

is divided

by the number

of

in Windows)

Mouser’s

personal

computer

follows

an exponential

distribuminenumber

the

p-value.

occurrences.

What

is

this

approach

to

probability

called?

tion

with

a

mean

of

27

seconds.

What

is

the

probability

his

“boot”

will

require:

Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a

26.

49. a.

The

probability

the cause

and the cure

for allthat

cancers

will be discovered

before

the

Less

than 15

seconds?

long

history,

thethat

production

department

reports

the distribution

of the bag

weights

year

2020

isnormal

.20.

What

viewpoint

of the

probability

does

this statement

illustrate?process is

b.

More

than

60 seconds?

follows

the

distribution

and

standard

deviation

of the packaging

Berdine’s

Chicken

Factory

several

stores

in the

Head,manager,

South Carolina,

50. c.

Between

30bag.

and

45the

seconds?

3 pounds

per

At

end of has

each

day, Jeff

Rutter,

theHilton

production

weighs

c. In thed.

dialog

box,

that thebelow

range of

Variable

1 isweight

area.

When

interviewing

applicants

for

server

positions,

the

owner

like to inWhat

isindicate

the

point

which

only

10%

ofofthe

boots

occur?

10

bags

and

computes

the

mean

the

sample.

Below

arewould

the weights

of

from A1

to A6 information

and Variable 2 from

to B7,

the Hypotheclude

onB1

the

of tip a server

to earn

per

check popula(or bill).

72.

between

visits

toamount

aAlpha

U.S.is emergency

roomcan

forexpect

a member

of the

general

10 bags

fromistoday’s

production.

sizedThe

Meantime

Difference

0, click

Labels,

0.05,

A Output

study

of 500

recent

indicated

server

theWhat

following

amounts

in

and the

Range

is D1.

Click OK. checks

tion

follows

an

exponential

distribution

withthe

a mean

ofearned

2.5 years.

proportion

of the

tips per 8-hour shift.

population:

45.6

47.7

47.6

46.3

46.2

47.4

49.2

55.8

47.5

48.5

a. Will visit an emergency room within the next 6 months?

b. Will not visit the ER over

theofnext

6 years?

Amount

a. Can Mr. Rutter conclude

that Tip

the mean weight ofNumber

the bags is less than 50 pounds?

c. Will visit an ER next year, but not this year?

Use the .01 significanceuplevel.

to $ 20

d. Find the first and third$0quartiles

of this distribution. 200

b. In a brief report, tell why

Mr.

the z distribution

as the test statistic.

20 upon

to aRutter

50 can use

100 an exponential

73. The times between failures

personal

computer follow

distribution

c. Compute the p-value.50 up to 100

75

with a mean of 300,000 hours. What is the probability of:

27. A new weight-watching100

company,

Weight Reducers International,

advertises that those

up to hours?

200

75

a. A failure in less than 100,000

who join will lose an average

of 10 pounds after the first

two weeks. The standard devior more

b. No failure in the next200

500,000

hours? CHAPTER 12 50

ation is 2.8 pounds. A random sample of

50 The

people

who joined

theof weight

reduction

12–1.

Excel350,000

commands

for

the test

variances on

page 391 are:

c. The next failure occurring

between 200,000

and

hours?

Total

datalevel

for U.S.of

25significance,

in column A and for

I-75we

in colprogram revealed a mean

loss of 9 pounds.a.AtEnter

thethe500

.05

can

d. What are the mean and standard deviation of umn

theB.time

failures?

Labelbetween

the two columns.

conclude that those joining Weight Reducers b.

willSelect

losethe

less

than

10

pounds?

Determine

Data tab on the top menu. Then, on the far right,

theWhat

p-value.

a.

is the probability of a tip of $200 or more?

select Data Analysis. Select F-Test: Two-Sample for

L Y T I 28.

C Sb.

thenof

click

OK.

Dole

Inc. is“$0

concerned

that“$20

the 16-ounce

sliced

pineapple mutually

is being

ArePineapple

the categories

up to $20,”

up toVariances,

$50,”can

and

so

on considered

c. The range of the first variable is A1:A8, and B1:B9 for the

overfilled.

Assume

the standard

deviation

of thesecond.

process

is

ounce.

The

quality-conexclusive?

Clickwww.mhhe.com/lind17e.)

on .03

Labels,

enter 0.05

for Alpha,

select D1 for

11–2. The

Minitab

commands

for

the

two-sample

t-test

on

page

368

(The data for these exercises are available at the text website:

thewere

Output

Range, and

click

OK.arithmetic

trolIfdepartment

tookassociated

a randomwith

sample

50 cans

and totaled,

found

that

the

mean

are:

c.

the probabilities

eachofoutcome

what

would

that total

be?

a. Put theweight

amount absorbed

by the Store

brand inAt

C1 the

and the

was

16.05

ounces.

5%

level

of

significance,

can we conclude

thatsold

the

d.

What

is

the

probability

of

a

tip

of

up

to

$50?

74.

Refer

to

the

North

Valley

Real

Estate

data,

which

report

information

on

homes

amount absorbed by the Name brand paper towel in C2.

mean

weight

greater

than

ounces?

Determine

e.

theis

probability

of a16

tip

of

less than

$200? the p-value.

theis

last

year.

b. Fromduring

the What

toolbar,

select

Stat,

Basic Statistics,

and

then

2-Sample,

and click

51.

Winning

allOK.three

Crown”

races of

is the

considered

thecomputed

greatestearlier

feat of

a.

The

mean

selling“Triple

price (in

$ thousands)

homes was

toabepedigree

$357.0,

c. In the next dialog box, select Samples in different colAfter

adeviation

successful

Kentucky

Derby,

Corn on

the Cob to

is estimate

a heavy favorite

at 2

with

standard

ofC2$160.7.

the normal

distribution

the percentumns,racehorse.

select

C1aStore

for the First

column and

Name of Use

the Second,

click

nextselling

to Assume

variances,

to 1

odds

toboxwin

the

Preakness

Stakes.

age

ofthe

homes

forequal

more

than $500.000. Compare this to the actual results. Is price

and click OK.

a. normally

If he is adistributed?

2 to 1 favorite

to win the

Belmont

as well,

what ishow

his probability

of

Try another

test.

If price Stakes

is normally

distributed,

many homes

winning

the aTriple

should

have

price Crown?

greater than the mean? Compare this to the actual number of homes.

b. Construct

What do a

his

chancesdistribution

for the Preakness

Stakes

to be in order for him to be

frequency

of price. What

do have

you observe?

“even

money”

to on

earn

themarket

Triple Crown?

b. The

mean

days

the

is 30 with a standard deviation of 10 days. Use

52. Thethe normal

first card selected

fromtoaestimate

standardthe

52-card

deck

a king.on the market more than

distribution

number

of ishomes

a. 24 days.

If it is returned

to the

is the

probability

that atest.

kingIfwill

beon

drawn

on the

Compare

thisdeck,

to thewhat

actual

results.

Try another

days

the market

second selection?

is normally

distributed, how many homes

should

be

on the market more than the

12–2. The Excel commands for the one-way ANOVA on page 400 are:

b. mean

If the number

king is not

replaced,

whatthis

is the

probability

that

king

will labeled

be

drawn

onWTA,

thePoof days?

Compare

to the

actual

of

homes.

Does

the normal

a. Key innumber

data

intoafour

columns

Northern,

cono, and Branson.

second selection?

Software Commands

Lin66360_ch10_318-352.indd 348

Software examples using Excel, MegaStat®, and Minitab are included throughout the text. The explanations of the

computer input commands are placed at

the end of the text in Appendix C.

Lin66360_ch07_209-249.indd 244

Lin66360_ch05_132-174.indd 168

11–3. The Excel commands for the paired t-test on page 373 are:

a. Enter the data into columns B and C (or any other two columns) in the spreadsheet, with the variable names in the

first row.

b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select t-Test: Paired Two Sample for

Means, and then click OK.

c. In the dialog box, indicate that the range of Variable 1 is

from B1 to B11 and Variable 2 from C1 to C11, the

Hypothesized Mean Difference is 0, click Labels, Alpha is

.05, and the Output Range is E1. Click OK.

1/14/17 7:02 AM

1/16/17 9:53 PM

b. Select the Data tab on the top menu. Then, on the far right,

select Data Analysis. Select ANOVA: Single Factor, then

click OK.

c. In the subsequent dialog box, make the input range A1:D8,

click on Grouped by Columns, click on Labels in first row,

the Alpha text box is 0.05, and finally select Output Range

as F1 and click OK.

1/14/17 8:29 AM

1/10/17 7:41 PM

780

Lin66360_appc_774-784.indd 780

1/20/17 10:28 AM

126

A REVIEW OF CHAPTERS 1–4

D A T A A N A LY T I C S

44.

Refer to the North Valley real estate data recorded on homes sold during the last

year. Prepare a report on the selling prices of the homes based on the answers to the

following questions.

a. Compute the minimum, maximum, median, and the first and the third quartiles of

price. Create a box plot. Comment on the distribution of home prices.

b. Develop a scatter diagram with price on the vertical axis and the size of the home on

the horizontal. Is there a relationship between these variables? Is the relationship

16–7 direct

a. or indirect?

c. For homes without a pool, develop a scatter

Rank diagram with price on the vertical axis

and the size of the home on the horizontal. Do the same for homes with a pool. How

2

do the relationships

between

price

x

y

x and size fory homes without

d a pool anddhomes

with a pool compare?

Refer 805

to the Baseball

that report information

on

League

45.

232016 data5.5

1

4.5the 30 Major

20.25

Baseball teams for the 2016 season.

777

62 opened, 3.0

9 of operation

−6.0for that stadium.

36.00 For

a. In the data

set, the year

is the first year

each team, use this variable to create a new variable, stadium age, by subtracting

820

60

8.5

8

0.5

0.25

the value of the variable, year opened, from the current year. Develop a box plot

with the 682

new variable,40

age. Are there

which of the stadiums

1.0 any outliers?

4 If so, −3.0

9.00 are

outliers?

777

70 create3.0

−7.0

49.00 the

b. Using the

variable, salary,

a box plot. 10

Are there any

outliers? Compute

quartiles810

using formula

of your

28(4–1). Write

7.0a brief summary

2

5.0analysis. 25.00

c. Draw a scatter diagram with the variable, wins, on the vertical axis and salary on the

805

30 your conclusions?

5.5

3

2.5

6.25

horizontal

axis. What are

d. Using the variable, wins, draw a dot plot. What can you conclude from this plot?

840

42

10.0

5

5.0

25.00

Refer to the Lincolnville School District bus data.

46.

a. Referring777

to the maintenance

cost3.0

variable, develop

plot. What are16.00

the mini55

7 a box

−4.0

mum, first quartile, median, third quartile, and maximum values? Are there any

51

8.5

6

2.5

6.25

outliers?820

b. Using the median maintenance cost, develop a contingency0table with bus

manufac193.00

turer as one variable and whether the maintenance cost was above or below the

median as the other variable. What are your conclusions?

Answers to Self-Review

The worked-out solutions to the Self-Reviews are provided at the end of the text in Appendix E.

17

17

6(193)

= −.170

10(99)

b. H0: ρ = 0; H1: ρ ≠ 0. Reject H0 if t < −2.306 or t > 2.306.

rs = 1 −

BY S E C TI O N

t = −.170√

Section Reviews

A REVIEW OF

China

A REVIEW OF CHAPTERS

1–4Produced 832.8% more steel than the US

130

CASES

The review also includes continuing

cases and several small cases that let

students make decisions using tools

and techniques from a variety of

chapters.

Practice Test

The Practice Test is intended to

give students an idea of content

that might appear on a test and

how the test might be structured.

The Practice Test includes both

objective questions and problems

covering the material studied in

the section.

*

CHAPTER 17

*

This section is a review of the

and terms

introduced in Chapters 1–4. Chapter 1 began by describing the

5.major

Referconcepts

to the following

diagram.

meaning and purpose of statistics. Next we described the different types of variables and the four levels of measurement.

Chapter 2 was concerned with describing a set of observations by organizing it into a frequency distribution and then

portraying the frequency distribution as a histogram or a frequency polygon. Chapter 3 began by describing measures of

location, such as the mean, 17–1

weighted mean,

1. median, geometric mean, and mode. This chapter also included measures of

dispersion, or spread. Discussed in this section

were the range,Amount

variance, and Index

standard

deviation. Chapter 4 included

Country

(Based=US)

several graphing techniques such as dot plots, box plots, and scatter diagrams. We also discussed the coefficient of skew0

40

80

160

ness, which reports the lack of symmetry in a China

set of data.

822.7120

932.8 200

Throughout this section we stressed the importance of statistical software, such as Excel and Minitab. Many computer

110.7

125.5

a. What ishow

theJapan

graph called?

outputs in these chapters demonstrated

quickly

and effectively a large data set can be organized into a frequency

b. What

the

median,

and first

third quartile

values?

United

States

88.2

100.0

distribution, several of the measures

of are

location

or measures

of and

variation

calculated,

and

the information presented in

c. Is the distribution positively skewed? Tell how you know.

graphical form.

India

86.5

98.1

d. Are there any outliers? If yes, estimate these values.

Russia the number of71.5

81.1

e. Can you determine

observations in the study?

After selected groups of chapters

(1–4, 5–7, 8 and 9, 10–12, 13 and

14, 15 and 16, and 17 and 18), a

Section Review is included. Much

like a review before an exam, these

include a brief overview of the chapters and problems for review.

Cases

10 − 2

= −0.488

1 − (−0.170) 2

A REVIEW OF CHAPTERS 1–4

129

H01–4

is not rejected. We have not shown a relationship

CHAPTERS

between the two tests.

17

17

2. a.

location,

charts

or draw graphs

2. There

Determine

thesales

mean

and median ofwho

the checking

markets.

are 40

representatives

call di- acA. create

Century

National

Banksuch as a cumulative frequency

distribution,

determine

the quartiles

count

balances.

Compare

theIndex

and thedemedian

on large-volume

customers,

such

asmean

the athletic

The following

case willand

appear

inYear

subsequent

reviewAverage

sec- rectlyHourly

Earnings

(1995

=

Base)

for both

men

and

women.

Develop

the

charts

and

write

balances

for

the

four

branches.

Is

there

a difference

partments

at

major

colleges

and

universities

and

tions. Assume that you work in the Planning Department of

the report

summarizing

theBank

yearly

employees

among

thefranchises.

branches? There

Be sureare

to 30

explain

the

difference

sports

sales

reprethe Century

National

andsalaries

report

Lamberg. You professional

1995toof Ms.

11.65

100.0

at Wildcat

Plumbing

Supply.

Does it appear that there are

the mean

the median

in your

report.

sentatives between

who represent

theand

company

to retail

stores

lowill need

to do some

Lin66360_ch04_094-131.indd

126data analysis and prepare a short writ2000

14.02

120.3

pay differences

on gender?

3. shopping

Determine

the and

range

and discounters

the standard

deviation

of

malls

large

such

as

ten report. based

Remember,

Mr. Selig is the president of the bank, cated in

the

checking

account

balances.

What

do

the

and Target.

2005

138.5first and

so you will

want to ensure

that your

report is complete and Kmart 16.13

C. Kimble

Products:

Is There

a Difference

quartiles

show? Determine

the the

coefficient

of

Upon third

his return

to corporate

headquarters,

CEO

accurate. A copy of the data appears

in

Appendix

A.6.

2013

19.97

171.4

In the

Commissions?

andfor

indicate

it shows.

Because

sales manager

a reportwhat

comparing

the comCentury National Bank has offices in several cities in asked the skewness

At thethe

January

national

sales

meeting,

the

CEO

of

Kimble

Mr. Selig

does

not

deal

with

statistics

daily,

include

a

2016

21.37

183.4

missions

earned

last

year

by

the

two

parts

of

the

sales

Midwest and the southeastern part of the United

Products

wasMr.

questioned

extensively

com-like to team. The brief

description

and interpretation

the standard

information

is reported

below. Write of

a brief

reStates.

Dan Selig,

presidentregarding

and CEO,the

would

pany policy

for

paying

commissions

to

its

sales

represen2016

Average

wage

Increased

83.4%

from

1995

deviation

and

other

measures.

port.

Would

you

conclude

that

there

is

a

difference?

Be

know the characteristics of his checking account customtatives.

The

company

sells sporting

goods

to two major

sure to include information in the report on both the ceners.

What

is the balance

of a typical

customer?

B. Wildcat Plumbing Supply Inc.:

How many other bank services do the checking

ac- tral tendency and dispersion of the two groups.

b.

Do We Have Gender Differences?

Commissions

Earned by Sales

count customers

use?Representatives

Do the customers use the ATM serWildcat Earned

Plumbing

Supply

has served the plumbing

Calling

on and,

Athletic

Departments

($) WhatYear

Commissions

by Sales

Representatives

vice

if so,

how often?

about debit cards?

Who Hourly

Average

Earnings

Index

(1995 – 2000 = Base)

needs

of Southwest

Calling

on

Large

Retailers ($) Arizona for more than 40 years.

them,

how69often

they used?

354uses87

1,676and

1,187

3,202are 680

39 1,683 1,106

The company was founded by Mr. Terrence

St. Julian

1995

To better

understand

customers,

Mr. Selig

883 3,140

299 2,197

175 159the1,105

434 615

149 asked 11.65

1,116 681 1,294

12 754 1,206 1,448 870 90.8

944 1,255

and is run today by his son Cory. The company has

Wendy

of 2000

planning,

1,168Ms.278

579Lamberg,

7 357director

252 1,602

2,321 to 4select

392 a sam- 14.02

1,213 1,291 719 934 1,313 1,083 899 850109.2

886 1,556

grown from a handful of employees to more than 500

ple

of

customers

and

prepare

a

report.

To

begin,

she

has

416 427 1,738 526 13 1,604 249 557 635 527

886 1,315 1,858 1,262 1,338 1,066 807 1,244 758 918

today. Cory is concerned about several

positions within

125.7

appointed a team from her staff.2005

You are the head of the 16.13

the company where he has men and women doing esteam and responsible for preparing

the report. You select a 19.97

2013

155.6

sentially

the

same

job

but

at

different

pay. To investirandom sample of 60 customers. In addition to the balance

gate, he collected the information below.

Suppose you

2016

166.5

PRA

C T Iaccount

CE T

T of last

in each

at E

theSend

month, you determine 21.37

are a student intern in the Accounting Department and

(1) the number of ATM (automatic teller machine) transac2016

Average

wage

Increased

86.5%

from

the

average

of

1995,

2000

have

been

given

the

task

to

write

a

report

summarizing

Theretions

is a practice

test

at

the

end

of

each

review

section.

The

tests

are

in

two

parts.

The

first

part

contains

several

objecin the last month; (2) the number of other bank serthe

situation.In most cases, it should take 30 to 45

tive questions,

usuallyaccount,

in a fill-in-the-blank

Theetc.)

second

problems.

vices (a savings

a certificate format.

of deposit,

the part is

minutes

to complete

test. Thethe

problems

require

calculator.

Check the answers in the Answer Section in the back of

customer

uses; the

(3) whether

customer

aadebit

card

17–2

1.hasa.

P1 =

($85/$75)(100)

113.3

Yearly =

Salary

($000)

Women

Men

the book.

(this is a bank service in which charges are made directly

to

Less than

2

0

= 30

112.5

P2 = ($45/$40)(100)

the customer’s account); and (4) whether or not interest

is

Part paid

1—Objective

30 up to 40

3

1

on the checking account. The sample includes cusPAtlanta,

= (113.3

+ 112.5)/2

tomers

fromof the

branches

in Cincinnati,

Ohio;analyzing,

1. The

science

collecting,

organizing,

presenting,

and interpreting

to 112.9

assist in

40 data

up to=

50

17

4

Georgia;

Louisville,

Kentucky;

and Erie, Pennsylvania.

.

making

effective

decisions

is called

50 up to =

60 113.0 1. 17

24

b.

P = ($130/$115)(100)

2. Methods of organizing, summarizing, and presenting data in an informative60

way

are

up to 70

8

21

1. Develop a graph or table that portrays the checking

$85(500) + $45(1,200)

.

called

70 up to 80

7

balances. What is the balance of a typical

c.customer?

P=

(100)2. 3

3. The entire set of individuals or objects of interest or the measurements obtained

from all

80 or more

0

3

$75(500)

+

$40(1,200)

Do many customers have more than $2,000 in their

individuals or objects of interest are called the

.

3.

accounts? Does it appear that there is a difference in

4. List the two types of variables.

$96,500

To kick off the project, Mr. Cory4.St. Julian held a meeting

the distribution of the accounts among the four

(100)

=and112.9

5. The number of bedrooms in a house is an example of=a

. (discrete

variable,

with

his staff

you were invited. At this meeting, it was

branches? Around what value do the account bal85,500

continuous variable, qualitative variable—pick one)

5. several measures of

suggested that you calculate

ances tend to cluster?

6. The jersey numbers of Major League Baseball players are an example of what level of

measurement?

6.

7. The classification of students by eye color is an example of what level of measurement?

7.

8. The sum of the differences between each value and the mean is always equal to what value? 8.

9. A set of data contained 70 observations. How many classes would the 2k method suggest to

construct a frequency distribution?

9.

10. What percent of the values in a data set are always larger than the median?

10.

11. The square of the standard deviation is the

.

11.

xi

17

1/10/17 7:4

C

18

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AC KN OWLE DG M E NTS

This edition of Statistical Techniques in Business and Economics is the product of many people: students, colleagues, reviewers, and

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West Virginia University

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SUNY Geneseo

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Central Michigan University

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Northeast Mississippi Community

College

John Beyers

University of Maryland

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University of North Carolina

Charlotte

Anna Terzyan

Loyola Marymount University

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El Paso Community College

Their suggestions and thorough reviews of the previous edition and the manuscript of this edition make this a better text.

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University, built new data sets and revised Smartbook. Rene Ordonez, Southern Oregon University,

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We also wish to thank the staff at McGraw-Hill. This includes Dolly Womack, Senior Brand Manager; Michele Janicek, Product Developer Coordinator; Camille Corum and Ryan McAndrews, Product

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xv

xvi

CONTENTS

EN

H A N C E M E NTS TO

STATI STI CA L TE C H N I QU E S

I N BUS I N E SS & E CO N O M I C S , 17E

MAJOR CHANGES MADE TO INDIVIDUAL

CHAPTERS:

CHAPTER 1 What Is Statistics?

CHAPTER 8 Sampling Methods and the Central

Limit Theorem

• New Data Analytics section with new data and questions.

• Revised Self-Review 1-2.

CHAPTER 9 Estimation and Confidence Intervals

• New Section describing Business Analytics and its integration

with the text.

• New Self-Review 9-3 problem description.

• Updated exercises 2, 3, 17, and 19.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 2 Describing Data: Frequency Tables,

Frequency Distributions, and Graphic Presentation

• Updated exercises 5, 6, 12, 14, 23, 24, 33, 41, 43, and 61.

CHAPTER 10 One-Sample Tests

of Hypothesis

• Revised chapter introduction.

• Revised the Example/Solutions using an airport, cell phone

parking lot as the context.

• Added more explanation about cumulative relative frequency

distributions.

• Revised the section on Type II error to include an additional

example.

• Updated exercises 47 and 48 using real data.

• New Type II error exercises, 23 and 24.

• New Data Analytics section with new data and questions.

• Updated exercises 19, 31, 32, and 43.

CHAPTER 3 Describing Data:

Numerical Measures

• Updated Self-Review 3-2.

• Updated Exercises 16, 18, 73, 77, and 82.

• New Data Analytics section with new data and questions.

CHAPTER 4 Describing Data: Displaying and

Exploring Data

• New Data Analytics section with new data and questions.

CHAPTER 11 Two-Sample Tests

of Hypothesis

• Updated exercises 5, 9, 12, 26, 27, 30, 32, 34, 40, 42,

and 46.

• New Data Analytics section with new data and questions.

CHAPTER 12 Analysis of Variance

• Updated exercise 22 with 2016 New York Yankee player

salaries.

• Revised Self-Reviews 12-1 and 12-3.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 5 A Survey of Probability Concepts

CHAPTER 13 Correlation and Linear Regression

• Revised the Example/Solution in the section on Bayes

Theorem.

• Added new conceptual formula, to relate the standard error

to the regression ANOVA table.

• Updated exercises 45 and 58 using real data.

• Updated exercises 36, 41, 42, 43, and 57.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

CHAPTER 6 Discrete Probability Distributions

CHAPTER 14 Multiple Regression Analysis

• Expanded discussion of random variables.

• Updated exercises 19, 21, 23, 24, and 25.

• Revised the Example/Solution in the section on Poisson

distribution.

• New Data Analytics section with new data and questions.

• Updated exercises 18, 58, and 68.

• New Data Analytics section with new data and questions.

CHAPTER 7 Continuous Probability Distributions

• Updated exercises 10, 21, 24, 33, 38, 42, and 44.

CHAPTER 15 Nonparametric Methods: Nominal

Level Hypothesis Tests

• Updated the context of Manelli Perfume Company Example/

Solution.

• Revised the Example/Solutions using Uber as the context.

• Revised the “Hypothesis Test of Unequal Expected Frequencies” Example/Solution.

• Updated exercises 19, 22, 28, 36, 47, and 64.

• Updated exercises 3, 31, 42, 46, and 61.

• New Data Analytics section with new data and questions.

• New Data Analytics section with new data and questions.

• Revised Self-Review 7-1.

xvi

CHAPTER 16 Nonparametric Methods: Analysis of

Ordinal Data

CHAPTER 18 Time Series and Forecasting

• Revised the “Sign Test” Example/Solution.

• New Data Analytics section with new data and questions.

• Revised the “Testing a Hypothesis About a Median” Example/

Solution.

• Revised the “Wilcoxon Rank-Sum Test for Independent Populations” Example/Solution.

• Revised Self-Reviews 16-3 and 16-6.

• Updated exercise 25.

• Updated dates, illustrations, and examples.

CHAPTER 19 Statistical Process Control and

Quality Management

• Updated 2016 Malcolm Baldridge National Quality Award

winners.

• Updated exercises 13, 22, and 25.

• New Data Analytics section with new data and questions.

CHAPTER 17 Index Numbers

• Revised Self-Reviews 17-1, 17-2, 17-3, 17-4, 17-5, 17-6, 17-7.

• Updated dates, illustrations, and examples.

• New Data Analytics section with new data and questions.

xvii

BRIEF CONTENTS

1 What is Statistics? 1

2 Describing Data: Frequency Tables, Frequency Distributions,

and Graphic Presentation

18

3 Describing Data: Numerical Measures 51

4 Describing Data: Displaying and Exploring Data 94

5 A Survey of Probability Concepts 132

6 Discrete Probability Distributions 175

7 Continuous Probability Distributions 209

8 Sampling Methods and the Central Limit Theorem

9 Estimation and Confidence Intervals 282

10 One-Sample Tests of Hypothesis 318

11 Two-Sample Tests of Hypothesis 353

12 Analysis of Variance 386

13 Correlation and Linear Regression 436

14 Multiple Regression Analysis 488

15 Nonparametric Methods:

Nominal Level Hypothesis Tests

16

7

1

18

19

20

Nonparametric Methods:

Analysis of Ordinal Data

Index Numbers

Review Section

250

Review Section

Review Section

Review Section

545

582

Review Section

621

Time Series and Forecasting

653

Review Section

Statistical Process Control and Quality Management

An Introduction to Decision Theory

Glossary

Index

697

728

Appendixes:

Data Sets, Tables, Software Commands, Answers

Review Section

745

847

851

xix

CONTENTS

A Note from the Authors

vi

1What is Statistics?

1

Introduction 2

Why Study Statistics? 2

What is Meant by Statistics? 3

E X E RC ISE S 41

Chapter Summary 42

Chapter Exercises 43

Data Analytics 49

Types of Statistics 4

Descriptive Statistics 4

Inferential Statistics 5

Types of Variables 6

Levels of Measurement 7

Nominal-Level Data 7

Ordinal-Level Data 8

Interval-Level Data 9

Ratio-Level Data 10

EX ERCISES 11

Ethics and Statistics 12

Basic Business Analytics 12

3Describing Data:

NUMERICAL MEASURES

51

Introduction 52

Measures of Location 52

The Population Mean 53

The Sample Mean 54

Properties of the Arithmetic

Mean 55

E X E RC ISE S 56

Chapter Summary 13

The Median 57

The Mode 59

Chapter Exercises 14

E X E RC ISE S 61

Data Analytics 17

The Relative Positions of the Mean,

Median, and Mode 62

E X E RC ISE S 63

2Describing Data:

FREQUENCY TABLES, FREQUENCY

DISTRIBUTIONS, AND GRAPHIC

PRESENTATION 18

E X E RC ISE S 66

The Geometric Mean 66

Introduction 19

E X E RC ISE S 68

Constructing Frequency Tables 19

Why Study Dispersion? 69

Relative Class Frequencies 20

Graphic Presentation

of Qualitative Data 21

EX ERCISES 25

Constructing Frequency

Distributions 26

Relative Frequency Distribution 30

EX ERCISES 31

Graphic Presentation of a Distribution 32

Histogram 32

Frequency Polygon 35

EX ERCISES 37

Cumulative Distributions 38

xx

Software Solution 64

The Weighted Mean 65

Range 70

Variance 71

E X E RC ISE S 73

Population Variance 74

Population Standard Deviation 76

E X E RC ISE S 76

Sample Variance and Standard

Deviation 77

Software Solution 78

E X E RC ISE S 79

Interpretation and Uses of the Standard

Deviation 79

Chebyshev’s Theorem 79

The Empirical Rule 80

xxi

CONTENTS

EXER C ISES 81

E X E RC ISE S 140

The Mean and Standard Deviation

of Grouped Data 82

Rules of Addition for Computing

Probabilities 141

Arithmetic Mean of Grouped Data 82

Standard Deviation of Grouped Data 83

EXER C ISES 85

Ethics and Reporting Results 86

E X E RC ISE S 146

Chapter Summary 86

Rules of Multiplication

to Calculate Probability 147

Pronunciation Key 88

Chapter Exercises 88

Data Analytics 92

Special Rule of Multiplication 147

General Rule of Multiplication 148

Contingency Tables 150

4Describing Data:

Special Rule of Addition 141

Complement Rule 143

The General Rule of Addition 144

DISPLAYING AND EXPLORING DATA 94

Tree Diagrams 153

E X E RC ISE S 155

Bayes’ Theorem 157

Introduction 95

E X E RC ISE S 161

Dot Plots 95

Principles of Counting 161

Stem-and-Leaf Displays 96

EXER C ISES 101

Measures of Position 103

Quartiles, Deciles, and Percentiles 103

EXER C ISES 106

The Multiplication Formula 161

The Permutation Formula 163

The Combination Formula 164

E X E RC ISE S 166

Chapter Summary 167

Pronunciation Key 168

Box Plots 107

Chapter Exercises 168

EXER C ISES 109

Data Analytics 173

Skewness 110

EXER C ISES 113

Describing the Relationship between

Two Variables 114

Contingency Tables 116

6Discrete Probability

Distributions 175

Introduction 176

EXER C ISES 118

Chapter Summary 119

What is a Probability Distribution? 176

Pronunciation Key 120

Random Variables 178

Chapter Exercises 120

Data Analytics 126

Discrete Random Variable 179

Continuous Random Variable 179

The Mean, Variance, and Standard Deviation of a

Discrete Probability Distribution 180

Problems 127

Cases 129

Mean 180

Variance and Standard Deviation 180

Practice Test 130

E X E RC ISE S 182

5A Survey of Probability

Concepts 132

Introduction 133

What is a Probability? 134

Approaches to Assigning Probabilities 136

Classical Probability 136

Empirical Probability 137

Subjective Probability 139

Binomial Probability Distribution 184

How Is a Binomial Probability

Computed? 185

Binomial Probability Tables 187

E X E RC ISE S 190

Cumulative Binomial Probability

Distributions 191

E X E RC ISE S 193

Hypergeometric Probability Distribution 193

xxiiCONTENTS

EX ERCISES 197

E X E RC ISE S 257

Poisson Probability Distribution 197

Sampling “Error” 259

EX ERCISES 202

Sampling Distribution of the Sample Mean 261

Chapter Summary 202

E X E RC ISE S 264

Chapter Exercises 203

The Central Limit Theorem 265

Data Analytics 208

7Continuous Probability

Distributions 209

Introduction 210

The Family of Uniform Probability

Distributions 210

EX ERCISES 213

The Family of Normal Probability Distributions 214

The Standard Normal Probability

Distribution 217

Applications of the Standard Normal

Distribution 218

The Empirical Rule 218

EX ERCISES 220

Finding Areas under the Normal Curve 221

EX ERCISES 224

EX ERCISES 226

EX ERCISES 229

The Normal Approximation

to the Binomial 229

Continuity Correction Factor 230

How to Apply the Correction Factor 232

EX ERCISES 233

The Family of Exponential Distributions 234

EX ERCISES 238

Chapter Summary 239

Chapter Exercises 240

Data Analytics 244

Problems 246

Cases 247

Practice Test 248

8Sampling Methods and the

Central Limit Theorem 250

Introduction 251

Sampling Methods 251

Reasons to Sample 251

Simple Random Sampling 252

Systematic Random Sampling 255

Stratified Random Sampling 255

Cluster Sampling 256

E X E RC ISE S 271

Using the Sampling Distribution of the

Sample Mean 273

E X E RC ISE S 275

Chapter Summary 275

Pronunciation Key 276

Chapter Exercises 276

Data Analytics 281

9Estimation and Confidence

Intervals 282

Introduction 283

Point Estimate for a Population Mean 283

Confidence Intervals for a Population Mean 284

Population Standard Deviation, Known σ 284

A Computer Simulation 289

E X E RC ISE S 291

Population Standard Deviation, σ Unknown 292

E X E RC ISE S 299

A Confidence Interval for a Population

Proportion 300

E X E RC ISE S 303

Choosing an Appropriate Sample Size 303

Sample Size to Estimate a Population Mean 304

Sample Size to Estimate a Population

Proportion 305

E X E RC ISE S 307

Finite-Population Correction Factor 307

E X E RC ISE S 309

Chapter Summary 310

Chapter Exercises 311

Data Analytics 315

Problems 316

Cases 317

Practice Test 317

10One-Sample Tests

of Hypothesis 318

Introduction 319

What is Hypothesis Testing? 319

xxiii

CONTENTS

Six-Step Procedure for Testing

a Hypothesis 320

Step 1: State the Null Hypothesis (H0) and the

Alternate Hypothesis (H1) 320

Step 2: Select a Level of Significance 321

Step 3: Select the Test Statistic 323

Step 4: Formulate the Decision Rule 323

Step 5: Make a Decision 324

Step 6: Interpret the Result 324

One-Tailed and Two-Tailed Hypothesis Tests 325

Hypothesis Testing for a Population Mean: Known

Population Standard Deviation 327

A Two-Tailed Test 327

A One-Tailed Test 330

p-Value in Hypothesis Testing 331

Chapter Exercises 378

Data Analytics 385

12Analysis of Variance

Introduction 387

Comparing Two Population Variances 387

The F Distribution 387

Testing a Hypothesis of Equal Population

Variances 388

E X E RC ISE S 391

ANOVA: Analysis of Variance 392

ANOVA Assumptions 392

The ANOVA Test 394

EXER C ISES 333

E X E RC ISE S 401

Hypothesis Testing for a Population Mean:

Population Standard Deviation Unknown 334

Inferences about Pairs of Treatment

Means 402

EXERC ISES 339

E X E RC ISE S 404

A Statistical Software Solution 340

Two-Way Analysis of Variance 406

EXERC ISES 342

E X E RC ISE S 411

Type II Error 343

Two-Way ANOVA with Interaction 412

EXERC ISES 346

Chapter Summary 347

Pronunciation Key 348

Chapter Exercises 348

Data Analytics 352

386

Interaction Plots 412

Testing for Interaction 413

Hypothesis Tests for Interaction 415

E X E RC ISE S 417

Chapter Summary 418

Pronunciation Key 420

11Two-Sample Tests

of Hypothesis 353

Chapter Exercises 420

Data Analytics 429

Problems 431

Introduction 354

Cases 433

Two-Sample Tests of Hypothesis: Independent

Samples 354

Practice Test 434

EXERC ISES 359

Comparing Population Means with Unknown

Population Standard Deviations 360

Two-Sample Pooled Test 360

EXERC ISES 364

Unequal Population Standard

Deviations 366

EXERC ISES 369

Two-Sample Tests of Hypothesis:

Dependent Samples 370

Comparing Dependent

and Independent Samples 373

EXERC ISES 375

13Correlation and

Linear Regression

436

Introduction 437

What is Correlation Analysis? 437

The Correlation Coefficient 440

E X E RC ISE S 445

Testing the Significance of the Correlation

Coefficient 447

E X E RC ISE S 450

Regression Analysis 451

Least Squares Principle 451

Drawing the Regression Line 454

Chapter Summary 377

E X E RC ISE S 457

Pronunciation Key 378

Testing the Significance of the Slope 459

xxivCONTENTS

EX ERCISES 461

Qualitative Independent Variables 512

Evaluating a Regression Equation’s

Ability to Predict 462

Regression Models with Interaction 515

Stepwise Regression 517

The Standard Error of Estimate 462

The Coefficient of Determination 463

E X E RC ISE S 519

Review of Multiple Regression 521

EX ERCISES 464

Chapter Summary 527

Relationships among the Correlation

Coefficient, the Coefficient of

Determination, and the Standard

Error of Estimate 464

Pronunciation Key 528

Chapter Exercises 529

Data Analytics 539

EX ERCISES 466

Problems 541

Interval Estimates of Prediction 467

Cases 542

Assumptions Underlying Linear

Regression 467

Constructing Confidence and Prediction

Intervals 468

EX ERCISES 471

Transforming Data 471

Practice Test 543

15Nonparametric Methods:

NOMINAL LEVEL HYPOTHESIS TESTS 545

EX ERCISES 474

Introduction 546

Chapter Summary 475

Pronunciation Key 477

Test a Hypothesis of a Population

Proportion 546

Chapter Exercises 477

E X E RC ISE S 549

Data Analytics 487

Two-Sample Tests about Proportions 550

E X E RC ISE S 554

14Multiple Regression

Analysis 488

Goodness-of-Fit Tests: Comparing Observed and

Expected Frequency Distributions 555

Hypothesis Test of Equal Expected

Frequencies 555

Introduction 489

E X E RC ISE S 560

Multiple Regression Analysis 489

Hypothesis Test of Unequal Expected

Frequencies 562

EX ERCISES 493

Evaluating a Multiple Regression Equation 495

Limitations of Chi-Square 563

The ANOVA Table 495

Multiple Standard Error of Estimate 496

Coefficient of Multiple Determination 497

Adjusted Coefficient of Determination 498

E X E RC ISE S 565

Testing the Hypothesis That a Distribution is

Normal 566

EX ERCISES 499

E X E RC ISE S 569

Inferences in Multiple Linear

Regression 499

Contingency Table Analysis 570

E X E RC ISE S 573

Global Test: Testing the Multiple

Regression Model 500

Evaluating Individual Regression

Coefficients 502

Chapter Summary 574

Pronunciation Key 575

Chapter Exercises 576

EX ERCISES 505

Data Analytics 581

Evaluating the Assumptions of Multiple

Regression 506

Linear Relationship 507

Variation in Residuals Same for Large

and Small ŷ Values 508

Distribution of Residuals 509

Multicollinearity 509

Independent Observations 511

16Nonparametric Methods:

ANALYSIS OF ORDINAL DATA 582

Introduction 583

The Sign Test 583

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