CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION

Entries in this table

give the area under the

curve to the left of the

z value. For example, for

z = –.85, the cumulative

probability is .1977.

Cumulative

probability

z

0

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

Ϫ3.0

.0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

Ϫ2.9

Ϫ2.8

Ϫ2.7

Ϫ2.6

Ϫ2.5

.0019

.0026

.0035

.0047

.0062

.0018

.0025

.0034

.0045

.0060

.0018

.0024

.0033

.0044

.0059

.0017

.0023

.0032

.0043

.0057

.0016

.0023

.0031

.0041

.0055

.0016

.0022

.0030

.0040

.0054

.0015

.0021

.0029

.0039

.0052

.0015

.0021

.0028

.0038

.0051

.0014

.0020

.0027

.0037

.0049

.0014

.0019

.0026

.0036

.0048

Ϫ2.4

Ϫ2.3

Ϫ2.2

Ϫ2.1

Ϫ2.0

.0082

.0107

.0139

.0179

.0228

.0080

.0104

.0136

.0174

.0222

.0078

.0102

.0132

.0170

.0217

.0075

.0099

.0129

.0166

.0212

.0073

.0096

.0125

.0162

.0207

.0071

.0094

.0122

.0158

.0202

.0069

.0091

.0119

.0154

.0197

.0068

.0089

.0116

.0150

.0192

.0066

.0087

.0113

.0146

.0188

.0064

.0084

.0110

.0143

.0183

Ϫ1.9

Ϫ1.8

Ϫ1.7

Ϫ1.6

Ϫ1.5

.0287

.0359

.0446

.0548

.0668

.0281

.0351

.0436

.0537

.0655

.0274

.0344

.0427

.0526

.0643

.0268

.0336

.0418

.0516

.0630

.0262

.0329

.0409

.0505

.0618

.0256

.0322

.0401

.0495

.0606

.0250

.0314

.0392

.0485

.0594

.0244

.0307

.0384

.0475

.0582

.0239

.0301

.0375

.0465

.0571

.0233

.0294

.0367

.0455

.0559

Ϫ1.4

Ϫ1.3

Ϫ1.2

Ϫ1.1

Ϫ1.0

.0808

.0968

.1151

.1357

.1587

.0793

.0951

.1131

.1335

.1562

.0778

.0934

.1112

.1314

.1539

.0764

.0918

.1093

.1292

.1515

.0749

.0901

.1075

.1271

.1492

.0735

.0885

.1056

.1251

.1469

.0721

.0869

.1038

.1230

.1446

.0708

.0853

.1020

.1210

.1423

.0694

.0838

.1003

.1190

.1401

.0681

.0823

.0985

.1170

.1379

Ϫ.9

Ϫ.8

Ϫ.7

Ϫ.6

Ϫ.5

.1841

.2119

.2420

.2743

.3085

.1814

.2090

.2389

.2709

.3050

.1788

.2061

.2358

.2676

.3015

.1762

.2033

.2327

.2643

.2981

.1736

.2005

.2296

.2611

.2946

.1711

.1977

.2266

.2578

.2912

.1685

.1949

.2236

.2546

.2877

.1660

.1922

.2206

.2514

.2843

.1635

.1894

.2177

.2483

.2810

.1611

.1867

.2148

.2451

.2776

Ϫ.4

Ϫ.3

Ϫ.2

Ϫ.1

Ϫ.0

.3446

.3821

.4207

.4602

.5000

.3409

.3783

.4168

.4562

.4960

.3372

.3745

.4129

.4522

.4920

.3336

.3707

.4090

.4483

.4880

.3300

.3669

.4052

.4443

.4840

.3264

.3632

.4013

.4404

.4801

.3228

.3594

.3974

.4364

.4761

.3192

.3557

.3936

.4325

.4721

.3156

.3520

.3897

.4286

.4681

.3121

.3483

.3859

.4247

.4641

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION

Cumulative

probability

0

Entries in the table

give the area under the

curve to the left of the

z value. For example, for

z = 1.25, the cumulative

probability is .8944.

z

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.0

.1

.2

.3

.4

.5000

.5398

.5793

.6179

.6554

.5040

.5438

.5832

.6217

.6591

.5080

.5478

.5871

.6255

.6628

.5120

.5517

.5910

.6293

.6664

.5160

.5557

.5948

.6331

.6700

.5199

.5596

.5987

.6368

.6736

.5239

.5636

.6026

.6406

.6772

.5279

.5675

.6064

.6443

.6808

.5319

.5714

.6103

.6480

.6844

.5359

.5753

.6141

.6517

.6879

.5

.6

.7

.8

.9

.6915

.7257

.7580

.7881

.8159

.6950

.7291

.7611

.7910

.8186

.6985

.7324

.7642

.7939

.8212

.7019

.7357

.7673

.7967

.8238

.7054

.7389

.7704

.7995

.8264

.7088

.7422

.7734

.8023

.8289

.7123

.7454

.7764

.8051

.8315

.7157

.7486

.7794

.8078

.8340

.7190

.7517

.7823

.8106

.8365

.7224

.7549

.7852

.8133

.8389

1.0

1.1

1.2

1.3

1.4

.8413

.8643

.8849

.9032

.9192

.8438

.8665

.8869

.9049

.9207

.8461

.8686

.8888

.9066

.9222

.8485

.8708

.8907

.9082

.9236

.8508

.8729

.8925

.9099

.9251

.8531

.8749

.8944

.9115

.9265

.8554

.8770

.8962

.9131

.9279

.8577

.8790

.8980

.9147

.9292

.8599

.8810

.8997

.9162

.9306

.8621

.8830

.9015

.9177

.9319

1.5

1.6

1.7

1.8

1.9

.9332

.9452

.9554

.9641

.9713

.9345

.9463

.9564

.9649

.9719

.9357

.9474

.9573

.9656

.9726

.9370

.9484

.9582

.9664

.9732

.9382

.9495

.9591

.9671

.9738

.9394

.9505

.9599

.9678

.9744

.9406

.9515

.9608

.9686

.9750

.9418

.9525

.9616

.9693

.9756

.9429

.9535

.9625

.9699

.9761

.9441

.9545

.9633

.9706

.9767

2.0

2.1

2.2

2.3

2.4

.9772

.9821

.9861

.9893

.9918

.9778

.9826

.9864

.9896

.9920

.9783

.9830

.9868

.9898

.9922

.9788

.9834

.9871

.9901

.9925

.9793

.9838

.9875

.9904

.9927

.9798

.9842

.9878

.9906

.9929

.9803

.9846

.9881

.9909

.9931

.9808

.9850

.9884

.9911

.9932

.9812

.9854

.9887

.9913

.9934

.9817

.9857

.9890

.9913

.9936

2.5

2.6

2.7

2.8

2.9

.9938

.9953

.9965

.9974

.9981

.9940

.9955

.9966

.9975

.9982

.9941

.9956

.9967

.9976

.9982

.9943

.9957

.9968

.9977

.9983

.9945

.9959

.9969

.9977

.9984

.9946

.9960

.9970

.9978

.9984

.9948

.9961

.9971

.9979

.9985

.9949

.9962

.9972

.9979

.9985

.9951

.9963

.9973

.9980

.9986

.9952

.9964

.9974

.9981

.9986

3.0

.9986

.9987

.9987

.9988

.9988

.9989

.9989

.9989

.9990

.9990

ESSENTIALS OF

STATISTICS FOR

BUSINESS AND

ECONOMICS ∞e

David R. Anderson

University of Cincinnati

Dennis J. Sweeney

University of Cincinnati

Thomas A. Williams

Rochester Institute of Technology

Dedicated to

Marcia, Cherri, and Robbie

Essentials of Statistics for Business and Economics, Fifth Edition

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

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COPYRIGHT © 2009, 2006

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Brief Contents

Preface xii

About the Authors xvi

Chapter 1 Data and Statistics 1

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 26

Chapter 3 Descriptive Statistics: Numerical Measures 80

Chapter 4 Introduction to Probability 140

Chapter 5 Discrete Probability Distributions 185

Chapter 6 Continuous Probability Distributions 224

Chapter 7 Sampling and Sampling Distributions 256

Chapter 8 Interval Estimation 293

Chapter 9 Hypothesis Tests 332

Chapter 10 Comparisons Involving Means, Experimental Design,

and Analysis of Variance 377

Chapter 11 Comparisons Involving Proportions and a Test

of Independence 430

Chapter 12 Simple Linear Regression 464

Chapter 13 Multiple Regression 532

Appendix A References and Bibliography 580

Appendix B Tables 581

Appendix C Summation Notation 608

Appendix D Self-Test Solutions and Answers to Even-Numbered

Exercises 610

Appendix E Using Excel Functions 640

Appendix F Computing p-Values Using Minitab and Excel 645

Index 649

Contents

Preface xii

About the Authors xvi

Chapter 1

Data and Statistics 1

Statistics in Practice: BusinessWeek 2

1.1 Applications in Business and Economics 3

Accounting 3

Finance 4

Marketing 4

Production 4

Economics 4

1.2 Data 5

Elements, Variables, and Observations 6

Scales of Measurement 6

Qualitative and Quantitative Data 7

Cross-Sectional and Time Series Data 7

1.3 Data Sources 10

Existing Sources 10

Statistical Studies 11

Data Acquisition Errors 12

1.4 Descriptive Statistics 13

1.5 Statistical Inference 15

1.6 Computers and Statistical Analysis 17

Summary 17

Glossary 18

Supplementary Exercises 19

Chapter 2

Descriptive Statistics: Tabular and Graphical

Presentations 26

Statistics in Practice: Colgate-Palmolive Company 27

2.1 Summarizing Qualitative Data 28

Frequency Distribution 28

Relative Frequency and Percent Frequency Distributions 29

Bar Graphs and Pie Charts 29

2.2 Summarizing Quantitative Data 34

Frequency Distribution 34

Relative Frequency and Percent Frequency Distributions 35

Dot Plot 36

Histogram 36

Cumulative Distributions 37

Ogive 39

v

Contents

2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 43

2.4 Crosstabulations and Scatter Diagrams 48

Crosstabulation 48

Simpson’s Paradox 51

Scatter Diagram and Trendline 52

Summary 57

Glossary 59

Key Formulas 60

Supplementary Exercises 60

Case Problem 1: Pelican Stores 66

Case Problem 2: Motion Picture Industry 67

Appendix 2.1 Using Minitab for Tabular and Graphical Presentations 68

Appendix 2.2 Using Excel for Tabular and Graphical Presentations 70

Chapter 3

Descriptive Statistics: Numerical Measures 80

Statistics in Practice: Small Fry Design 81

3.1 Measures of Location 82

Mean 82

Median 83

Mode 84

Percentiles 85

Quartiles 86

3.2 Measures of Variability 90

Range 91

Interquartile Range 91

Variance 91

Standard Deviation 94

Coefficient of Variation 94

3.3 Measures of Distribution Shape, Relative Location, and Detecting

Outliers 97

Distribution Shape 97

z-Scores 98

Chebyshev’s Theorem 99

Empirical Rule 100

Detecting Outliers 101

3.4 Exploratory Data Analysis 104

Five-Number Summary 104

Box Plot 105

3.5 Measures of Association Between Two Variables 109

Covariance 109

Interpretation of the Covariance 111

Correlation Coefficient 113

Interpretation of the Correlation Coefficient 114

3.6 The Weighted Mean and Working with Grouped Data 118

Weighted Mean 118

Grouped Data 119

Summary 123

Glossary 124

Key Formulas 125

Supplementary Exercises 127

Case Problem 1: Pelican Stores 130

vi

Contents

Case Problem 2: Motion Picture Industry 132

Case Problem 3: Business Schools of Asia-Pacific 132

Appendix 3.1 Descriptive Statistics Using Minitab 134

Appendix 3.2 Descriptive Statistics Using Excel 136

Chapter 4

Introduction to Probability 140

Statistics in Practice: Rohm and Hass Company 141

4.1 Experiments, Counting Rules, and Assigning Probabilities 142

Counting Rules, Combinations, and Permutations 143

Assigning Probabilities 147

Probabilities for the KP&L Project 149

4.2 Events and Their Probabilities 152

4.3 Some Basic Relationships of Probability 156

Complement of an Event 156

Addition Law 157

4.4 Conditional Probability 162

Independent Events 166

Multiplication Law 166

4.5 Bayes’ Theorem 170

Tabular Approach 174

Summary 176

Glossary 176

Key Formulas 177

Supplementary Exercises 178

Case Problem: Hamilton County Judges 182

Chapter 5

Discrete Probability Distributions 185

Statistics in Practice: Citibank 186

5.1 Random Variables 186

Discrete Random Variables 187

Continuous Random Variables 188

5.2 Discrete Probability Distributions 189

5.3 Expected Value and Variance 195

Expected Value 195

Variance 195

5.4 Binomial Probability Distribution 199

A Binomial Experiment 200

Martin Clothing Store Problem 201

Using Tables of Binomial Probabilities 205

Expected Value and Variance for the Binomial Distribution 206

5.5 Poisson Probability Distribution 210

An Example Involving Time Intervals 210

An Example Involving Length or Distance Intervals 212

5.6 Hypergeometric Probability Distribution 213

Summary 216

Glossary 217

Key Formulas 218

Supplementary Exercises 219

Appendix 5.1 Discrete Probability Distributions with Minitab 221

Appendix 5.2 Discrete Probability Distributions with Excel 222

vii

Contents

Chapter 6

Continuous Probability Distributions 224

Statistics in Practice: Procter & Gamble 225

6.1 Uniform Probability Distribution 226

Area as a Measure of Probability 227

6.2 Normal Probability Distribution 230

Normal Curve 230

Standard Normal Probability Distribution 232

Computing Probabilities for Any Normal Probability Distribution 237

Grear Tire Company Problem 238

6.3 Normal Approximation of Binomial Probabilities 242

6.4 Exponential Probability Distribution 245

Computing Probabilities for the Exponential Distribution 246

Relationship Between the Poisson and Exponential Distributions 247

Summary 249

Glossary 249

Key Formulas 250

Supplementary Exercises 250

Case Problem: Specialty Toys 253

Appendix 6.1 Continuous Probability Distributions with Minitab 254

Appendix 6.2 Continuous Probability Distributions with Excel 255

Chapter 7

Sampling and Sampling Distributions 256

Statistics in Practice: Meadwestvaco Corporation 257

7.1 The Electronics Associates Sampling Problem 258

7.2 Selecting a Sample 259

Sampling from a Finite Population 259

Sampling from a Process 261

7.3 Point Estimation 263

Practical Advice 264

7.4 Introduction to Sampling _Distributions 266

7.5 Sampling Distribution

_ of x 269

Expected Value of x 269

_

Standard Deviation of x 270

_

Form of the Sampling Distribution

of x 271

_

Sampling Distribution of x for the EAI Problem_ 272

Practical Value of the Sampling Distribution of x 273

Relationship Between

the Sample Size and the Sampling

_

Distribution of x 274 _

7.6 Sampling Distribution

_ of p 278

Expected Value of p 279

_

Standard Deviation of p 279

_

Form of the Sampling Distribution of p 280 _

Practical Value of the Sampling Distribution of p 281

7.7 Other Sampling Methods 284

Stratified Random Sampling 284

Cluster Sampling 285

Systematic Sampling 285

Convenience Sampling 286

Judgment Sampling 286

viii

Contents

Summary 287

Glossary 287

Key Formulas 288

Supplementary Exercises 288

Appendix 7.1 Random Sampling with Minitab 290

Appendix 7.2 Random Sampling with Excel 291

Chapter 8

Interval Estimation 293

Statistics in Practice: Food Lion 294

8.1 Population Mean: Known 295

Margin of Error and the Interval Estimate 295

Practical Advice 299

8.2 Population Mean: Unknown 301

Margin of Error and the Interval Estimate 302

Practical Advice 305

Using a Small Sample 305

Summary of Interval Estimation Procedures 307

8.3 Determining the Sample Size 310

8.4 Population Proportion 313

Determining the Sample Size 315

Summary 318

Glossary 319

Key Formulas 320

Supplementary Exercises 320

Case Problem 1: Young Professional Magazine 323

Case Problem 2: Gulf Real Estate Properties 324

Case Problem 3: Metropolitan Research, Inc. 326

Appendix 8.1 Interval Estimation with Minitab 326

Appendix 8.2 Interval Estimation Using Excel 328

Chapter 9

Hypothesis Tests 332

Statistics in Practice: John Morrell & Company 333

9.1 Developing Null and Alternative Hypotheses 334

Testing Research Hypotheses 334

Testing the Validity of a Claim 334

Testing in Decision-Making Situations 335

Summary of Forms for Null and Alternative Hypotheses 335

9.2 Type I and Type II Errors 336

9.3 Population Mean: Known 339

One-Tailed Tests 339

Two-Tailed Test 345

Summary and Practical Advice 348

Relationship Between Interval Estimation and Hypothesis Testing 349

9.4 Population Mean: Unknown 353

One-Tailed Tests 354

Two-Tailed Test 355

Summary and Practical Advice 356

ix

Contents

9.5 Population Proportion 359

Summary 362

Summary 364

Glossary 365

Key Formulas 366

Supplementary Exercises 366

Case Problem 1: Quality Associates, Inc. 368

Case Problem 2: Unemployment Study 370

Appendix 9.1 Hypothesis Testing with Minitab 370

Appendix 9.2 Hypothesis Testing with Excel 372

Chapter 10

Comparisons Involving Means, Experimental Design,

and Analysis of Variance 377

Statistics in Practice: U.S. Food and Drug Administration 378

10.1 Inferences About the Difference Between Two Population Means:

1 and 2 Known 379

Interval Estimation of 1 Ϫ 2 379

Hypothesis Tests About 1 Ϫ 2 381

Practical Advice 383

10.2 Inferences About the Difference Between Two Population Means:

1 and 2 Unknown 386

Interval Estimation of 1 Ϫ 2 386

Hypothesis Tests About 1 Ϫ 2 387

Practical Advice 390

10.3 Inferences About the Difference Between Two Population Means:

Matched Samples 394

10.4 An Introduction to Experimental Design and Analysis of Variance 400

Data Collection 401

Assumptions for Analysis of Variance 402

Analysis of Variance: A Conceptual Overview 403

10.5 Analysis of Variance and the Completely Randomized Design 405

Between-Treatments Estimate of Population Variance 406

Within-Treatments Estimate of Population Variance 407

Comparing the Variance Estimates: The F Test 408

ANOVA Table 410

Computer Results for Analysis of Variance 411

Testing for the Equality of k Population Means: An Observational

Study 412

Summary 416

Glossary 416

Key Formulas 417

Supplementary Exercises 419

Case Problem 1: Par, Inc. 423

Case Problem 2: Wentworth Medical Center 423

Case Problem 3: Compensation for Sales Professionals 424

Appendix 10.1 Inferences About Two Populations Using Minitab 425

Appendix 10.2 Inferences About Two Populations Using Excel 427

Appendix 10.3 Analysis of Variance with Minitab 428

Appendix 10.4 Analysis of Variance with Excel 429

x

Contents

Chapter 11

Comparisons Involving Proportions and a Test

of Independence 430

Statistics in Practice: United Way 431

11.1 Inferences About the Difference Between Two Population Proportions 432

Interval Estimation of p1 Ϫ p2 432

Hypothesis Tests About p1 Ϫ p2 434

11.2 Hypothesis Test for Proportions of a Multinomial Population 438

11.3 Test of Independence 445

Summary 452

Glossary 453

Key Formulas 453

Supplementary Exercises 454

Case Problem: A Bipartisan Agenda for Change 459

Appendix 11.1 Inferences About Two Population Proportions Using Minitab 459

Appendix 11.2 Tests of Goodness of Fit and Independence Using Minitab 460

Appendix 11.3 Tests of Goodness of Fit and Independence Using Excel 461

Chapter 12

Simple Linear Regression 464

Statistics in Practice: Alliance Data Systems 465

12.1 Simple Linear Regression Model 466

Regression Model and Regression Equation 466

Estimated Regression Equation 467

12.2 Least Squares Method 469

12.3 Coefficient of Determination 480

Correlation Coefficient 483

12.4 Model Assumptions 487

12.5 Testing for Significance 489

Estimate of 2 489

t Test 490

Confidence Interval for 1 491

F Test 492

Some Cautions About the Interpretation of Significance Tests 494

12.6 Using the Estimated Regression Equation for Estimation and Prediction 498

Point Estimation 498

Interval Estimation 498

Confidence Interval for the Mean Value of y 499

Prediction Interval for an Individual Value of y 500

12.7 Computer Solution 504

12.8 Residual Analysis: Validating Model Assumptions 509

Residual Plot Against x 510

Residual Plot Against yˆ 512

Summary 515

Glossary 515

Key Formulas 516

Supplementary Exercises 518

Case Problem 1: Measuring Stock Market Risk 524

Case Problem 2: U.S. Department of Transportation 525

Case Problem 3: Alumni Giving 526

Case Problem 4: Major League Baseball Team Values 526

Appendix 12.1 Regression Analysis with Minitab 528

Appendix 12.2 Regression Analysis with Excel 529

xi

Contents

Chapter 13

Multiple Regression 532

Statistics in Practice: International Paper 533

13.1 Multiple Regression Model 534

Regression Model and Regression Equation 534

Estimated Multiple Regression Equation 534

13.2 Least Squares Method 535

An Example: Butler Trucking Company 536

Note on Interpretation of Coefficients 538

13.3 Multiple Coefficient of Determination 544

13.4 Model Assumptions 547

13.5 Testing for Significance 548

F Test 548

t Test 551

Multicollinearity 552

13.6 Using the Estimated Regression Equation for Estimation and Prediction 555

13.7 Qualitative Independent Variables 558

An Example: Johnson Filtration, Inc. 558

Interpreting the Parameters 560

More Complex Qualitative Variables 562

Summary 566

Glossary 566

Key Formulas 567

Supplementary Exercises 568

Case Problem 1: Consumer Research, Inc. 573

Case Problem 2: Predicting Student Proficiency Test Scores 574

Case Problem 3: Alumni Giving 574

Case Problem 4: Predicting Winning Percentage for the NFL 576

Appendix 13.1 Multiple Regression with Minitab 577

Appendix 13.2 Multiple Regression with Excel 577

Appendix A

References and Bibliography 580

Appendix B

Tables 581

Appendix C

Summation Notation 608

Appendix D

Self-Test Solutions and Answers to Even-Numbered

Exercises 610

Appendix E

Using Excel Functions 640

Appendix F

Computing p-Values Using Minitab and Excel 645

Index 649

Preface

The purpose of ESSENTIALS OF STATISTICS FOR BUSINESS AND ECONOMICS is

to give students, primarily those in the fields of business administration and economics,

a conceptual introduction to the field of statistics and its many applications. The text is

applications-oriented and written with the needs of the nonmathematician in mind; the mathematical prerequisite is knowledge of algebra.

Applications of data analysis and statistical methodology are an integral part of the organization and presentation of the text material. The discussion and development of each

technique is presented in an application setting, with the statistical results providing insights

to decisions and solutions to problems.

Although the book is applications-oriented, we have taken care to provide sound

methodological development and to use notation that is generally accepted for the topic being covered. Hence, students will find that this text provides good preparation for the study

of more advanced statistical material. A bibliography to guide further study is included as

an appendix.

The text introduces the student to the statistical software packages of Minitab® 15 and

Microsoft® Office Excel® 2007 and emphasizes the role of computer software in the application of statistical analysis. Minitab is illustrated as it is one of the leading statistical software packages for both education and statistical practice. Excel is not a statistical software

package, but the wide availability and use of Excel makes it important for students to understand the statistical capabilities of this package. Minitab and Excel procedures are provided in appendices so that instructors have the flexibility of using as much computer

emphasis as desired for the course.

Changes in the Fifth Edition

We appreciate the acceptance and positive response to the previous editions of ESSENTIALS OF STATISTICS FOR BUSINESS AND ECONOMICS. Accordingly, in making modifications for this new edition, we have maintained the presentation style and readability of

those editions. The significant changes in the new edition are summarized here.

Content Revisions

The following list summarizes selected content revisions for the new edition.

• p-Values. In the previous edition, we emphasized the use of p-values as the preferred

approach to hypothesis testing. We continue this approach in the new edition. However, we have eased the introduction to p-values by simplifying the conceptual

definition for the student. We now say, “A p-value is a probability that provides a

measure of the evidence against the null hypothesis provided by the sample. The

smaller the p-value, the more evidence there is against H0.” After this conceptual

definition, we provide operational definitions that make it clear how the p-value is

computed for a lower tail test, an upper tail test, and a two-tail test. Based on our

experience, we have found that separating the conceptual definition from the operational definitions is helpful to the novice student trying to digest difficult new

material.

xiii

Preface

• Minitab and Excel Procedures for Computing p-Values. New to this edition is

•

•

an appendix showing how Minitab and Excel can be used to compute p-values associated with z, t, 2, and F test statistics. Students who use hand calculations to

compute the value of test statistics will be shown how statistical tables can be used

to provide a range for the p-value. Appendix F provides a means for these students

to compute the exact p-value using Minitab or Excel. This appendix will be helpful

for the coverage of hypothesis testing in Chapters 9 through 13.

Cumulative Standard Normal Distribution Table. It may be a surprise to many

of our users, but in the new edition we use the cumulative standard normal distribution table. We are making this change because of what we believe is the growing

trend for more and more students and practitioners alike to use statistics in an environment that emphasizes modern computer software. Historically, a table was used

by everyone because a table was the only source of information about the normal

distribution. However, many of today’s students are ready and willing to learn about

the use of computer software in statistics. Students will find that virtually every

computer software package uses the cumulative standard normal distribution. Thus,

it is becoming more and more important for introductory statistical texts to use a

normal probability table that is consistent with what the student will see when working with statistical software. It is no longer desirable to use one form of the standard

normal distribution table in the text and then use a different type of standard normal

distribution calculation when using a software package. Those who are using the cumulative normal distribution table for the first time will find that, in general, it eases

the normal probability calculations. In particular, a cumulative normal probability

table makes it easier to compute p-values for hypothesis testing.

Other Content Revisions. The following additional content revisions appear in the

new edition.

• Statistical routines covered in the chapter-ending appendices feature Minitab 15

and Excel 2007 procedures.

• New examples of time series data are provided in Chapter 1.

• The Excel appendix to Chapter 2 now provides more complete instructions on

how to develop a frequency distribution and a histogram for quantitative data.

• The introduction of sampling in Chapter 7 covers simple random sampling from

finite populations and random sampling from a process.

• Revised guidelines on the sample size necessary to use the t distribution now provide a consistency for the use of the t distribution in Chapters 8, 9, and 10.

• Step-by-step summary boxes for computing p-values for one-tailed and twotailed hypothesis tests are included in Chapter 9.

• Sections 10.4 and 10.5 have been revised to include an introduction to experimental design concepts. We show how analysis of variance (ANOVA) can be

used to analyze data from a completely randomized design as well as continue

to show how ANOVA can be used for the comparison of k means in an observational study.

• The Solutions Manual now shows the exercise solution steps using the cumulative normal distribution and more details in the explanations about how to compute p-values for hypothesis testing.

New Examples and Exercises Based on Real Data

We have added approximately 150 new examples and exercises based on real data and recent reference sources of statistical information. Using data pulled from sources also used

by the Wall Street Journal, USA Today, Fortune, Barron’s, and a variety of other sources,

we have drawn actual studies to develop explanations and to create exercises that demonstrate

many uses of statistics in business and economics. We believe that the use of real data helps

xiv

Preface

generate more student interest in the material and enables the student to learn about both

the statistical methodology and its application. The fifth edition of the text contains

approximately 300 examples and exercises based on real data.

New Case Problems

We have added five new case problems to this edition, bringing the total number of case

problems in the text to twenty-three. The new case problems appear in the chapters on descriptive statistics, interval estimation, and regression. These case problems provide students with the opportunity to analyze somewhat larger data sets and prepare managerial

reports based on the results of the analysis.

Features and Pedagogy

We have continued many of the features that appeared in previous editions. Some of the important ones are noted here.

Statistics in Practice

Each chapter begins with a Statistics in Practice article that describes an application of the

statistical methodology to be covered in the chapter. New to this edition are Statistics in

Practice articles for Rohm and Hass Company in Chapter 4 and the U.S. Food and Drug

Administration in Chapter 10.

Methods Exercises and Applications Exercises

The end-of-section exercises are split into two parts, Methods and Applications. The Methods exercises require students to use the formulas and make the necessary computations.

The Applications exercises require students to use the chapter material in real-world situations. Thus, students first focus on the computational “nuts and bolts,” then move on to the

subtleties of statistical application and interpretation.

Self-Test Exercises

Certain exercises are identified as self-test exercises. Completely worked-out solutions for

those exercises are provided in Appendix D at the back of the book. Students can attempt

the self-test exercises and immediately check the solution to evaluate their understanding

of the concepts presented in the chapter.

Margin Annotations and Notes and Comments

Margin annotations that highlight key points and provide additional insights for the student

are a key feature of this text. These annotations are designed to provide emphasis and enhance understanding of the terms and concepts being presented in the text.

At the end of many sections, we provide Notes and Comments designed to give the student additional insights about the statistical methodology and its application. Notes and

Comments include warnings about or limitations of the methodology, recommendations for

application, brief descriptions of additional technical considerations, and other matters.

Minitab and Excel® Appendices

Optional Minitab and Excel appendices appear at the end of most chapters. These appendices provide step-by-step instructions that make it easy for students to use Minitab or Excel

xv

Preface

to conduct the statistical analysis presented in the chapter. The appendices in this edition

provide instructions for twenty-eight statistical routines and feature Minitab 15 and Excel

2007 procedures.

Data Sets Accompany the Text

Over 160 data sets are now available on the CD-ROM that is packaged with the text. The

data sets are available in both Minitab and Excel formats. Data set logos are used in the text

to identify the data sets that are available on the CD. Data sets for all case problems as well

as data sets for larger exercises are also included on the CD.

Get Choice and Flexibility with

ThomsonNOW™

Designed by instructors and students for instructors and students, ThomsonNOW for Essentials of Statistics for Business and Economics is the most reliable, flexible, and easy-touse online suite of services and resources. With efficient and immediate paths to success,

ThomsonNOW delivers the results you expect.

• Personalized learning plans. For every chapter, personalized learning plans allow

•

•

students to focus on what they still need to learn and to select the activities that best

match their learning styles (such as animations, step-by-step problem demonstrations, and text pages).

More study options. Students can choose how they read the textbook—via integrated digital eBook or by reading the print version.

Information. Students can find more information and purchase ThomsonNow online. Go to http://www.thomsonedu.com/ and click on ThomsonNOW.

Ancillaries for Students

A Student CD is packaged free with each new text. It provides over 160 data files, and they

are available in both Minitab and Excel formats. Data sets for all case problems, as well as

data sets for larger exercises, are included.

Acknowledgments

A special thanks goes to our associates from business and industry who supplied the Statistics in Practice features. We recognize them individually by a credit line in each of the

articles. Finally, we are also indebted to our senior acquisitions editor Charles McCormick,

Jr., our senior developmental editor Alice Denny and developmental editor Maggie

Kubale, our content project managers Patrick Cosgrove and Amy Hackett, our senior marketing manager Larry Qualls, our technology project manager John Rich, and others at

Thomson/South-Western for their editorial counsel and support during the preparation of

this text.

David R. Anderson

Dennis J. Sweeney

Thomas A. Williams

About the Authors

David R. Anderson. David R. Anderson is Professor of Quantitative Analysis in the College of Business Administration at the University of Cincinnati. Born in Grand Forks, North

Dakota, he earned his B.S., M.S., and Ph.D. degrees from Purdue University. Professor

Anderson has served as Head of the Department of Quantitative Analysis and Operations

Management and as Associate Dean of the College of Business Administration. In addition, he

was the coordinator of the College’s first Executive Program.

At the University of Cincinnati, Professor Anderson has taught introductory statistics

for business students as well as graduate-level courses in regression analysis, multivariate

analysis, and management science. He has also taught statistical courses at the Department

of Labor in Washington, D.C. He has been honored with nominations and awards for

excellence in teaching and excellence in service to student organizations.

Professor Anderson has coauthored ten textbooks in the areas of statistics, management

science, linear programming, and production and operations management. He is an active

consultant in the field of sampling and statistical methods.

Dennis J. Sweeney. Dennis J. Sweeney is Professor of Quantitative Analysis and Founder

of the Center for Productivity Improvement at the University of Cincinnati. Born in Des

Moines, Iowa, he earned a B.S.B.A. degree from Drake University and his M.B.A. and

D.B.A. degrees from Indiana University, where he was an NDEA Fellow. During 1978–79,

Professor Sweeney worked in the management science group at Procter & Gamble; during

1981–82, he was a visiting professor at Duke University. Professor Sweeney served as Head

of the Department of Quantitative Analysis and as Associate Dean of the College of

Business Administration at the University of Cincinnati.

Professor Sweeney has published more than thirty articles and monographs in the area

of management science and statistics. The National Science Foundation, IBM, Procter &

Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded

his research, which has been published in Management Science, Operations Research,

Mathematical Programming, Decision Sciences, and other journals.

Professor Sweeney has coauthored ten textbooks in the areas of statistics, management

science, linear programming, and production and operations management.

Thomas A. Williams. Thomas A. Williams is Professor of Management Science in the

College of Business at Rochester Institute of Technology. Born in Elmira, New York, he

earned his B.S. degree at Clarkson University. He did his graduate work at Rensselaer

Polytechnic Institute, where he received his M.S. and Ph.D. degrees.

Before joining the College of Business at RIT, Professor Williams served for seven

years as a faculty member in the College of Business Administration at the University of

Cincinnati, where he developed the undergraduate program in Information Systems and

then served as its coordinator. At RIT he was the first chairman of the Decision Sciences

Department. He teaches courses in management science and statistics, as well as graduate

courses in regression and decision analysis.

Professor Williams is the coauthor of eleven textbooks in the areas of management

science, statistics, production and operations management, and mathematics. He has been

a consultant for numerous Fortune 500 companies and has worked on projects ranging from

the use of data analysis to the development of large-scale regression models.

CHAPTER

Data and Statistics

CONTENTS

Scales of Measurement

Qualitative and Quantitative Data

Cross-Sectional and Time

Series Data

STATISTICS IN PRACTICE:

BUSINESSWEEK

1.1

1.2

APPLICATIONS IN BUSINESS

AND ECONOMICS

Accounting

Finance

Marketing

Production

Economics

DATA

Elements, Variables, and

Observations

1.3

DATA SOURCES

Existing Sources

Statistical Studies

Data Acquisition Errors

1.4

DESCRIPTIVE STATISTICS

1.5

STATISTICAL INFERENCE

1.6

COMPUTERS AND

STATISTICAL ANALYSIS

1

2

Chapter 1

STATISTICS

Data and Statistics

in PRACTICE

BUSINESSWEEK*

NEW YORK, NEW YORK

With a global circulation of more than 1 million, BusinessWeek is the most widely read business magazine in

the world. More than 200 dedicated reporters and editors

in 26 bureaus worldwide deliver a variety of articles of

interest to the business and economic community. Along

with feature articles on current topics, the magazine

contains regular sections on International Business, Economic Analysis, Information Processing, and Science &

Technology. Information in the feature articles and the

regular sections helps readers stay abreast of current developments and assess the impact of those developments

on business and economic conditions.

Most issues of BusinessWeek provide an in-depth

report on a topic of current interest. Often, the in-depth

reports contain statistical facts and summaries that help

the reader understand the business and economic information. For example, the April 24, 2006, issue included

a special report on the world’s most innovative companies; the December 25, 2006, issue provided advice on

where to invest in 2007; and the January 8, 2007, issue

contained a feature article about business travel. In

addition, the weekly BusinessWeek Investor provides

statistics about the state of the economy, including production indexes, stock prices, mutual funds, and interest

rates.

BusinessWeek also uses statistics and statistical information in managing its own business. For example,

an annual survey of subscribers helps the company learn

about subscriber demographics, reading habits, likely

purchases, lifestyles, and so on. BusinessWeek managers

use statistical summaries from the survey to provide

*The authors are indebted to Charlene Trentham, Research Manager at

BusinessWeek, for providing this Statistics in Practice.

BusinessWeek uses statistical facts and summaries

in many of its articles. © Terri Miller/E-Visual

Communications, Inc.

better services to subscribers and advertisers. One recent

North American subscriber survey indicated that 90% of

BusinessWeek subscribers use a personal computer at

home and that 64% of BusinessWeek subscribers are

involved with computer purchases at work. Such statistics alert BusinessWeek managers to subscriber interest

in articles about new developments in computers. The

results of the survey are also made available to potential

advertisers. The high percentage of subscribers using

personal computers at home and the high percentage of

subscribers involved with computer purchases at work

would be an incentive for a computer manufacturer to

consider advertising in BusinessWeek.

In this chapter, we discuss the types of data available

for statistical analysis and describe how the data are obtained. We introduce descriptive statistics and statistical

inference as ways of converting data into meaningful

and easily interpreted statistical information.

Frequently, we see the following types of statements in newspapers and magazines:

• The National Association of Realtors reported that the median selling price for

•

a house in the United States was $222,600 (The Wall Street Journal, January 2,

2007).

The average cost of a 30-second television commercial during the 2006 Super Bowl

game was $2.5 million (USA Today, January 27, 2006).

1.1

Applications in Business and Economics

3

• A Jupiter Media survey found 31% of adult males watch television 10 or more hours

a week. For adult women it was 26% (The Wall Street Journal, January 26, 2004).

• General Motors, a leader in automotive cash rebates, provided an average cash

incentive of $4300 per vehicle (USA Today, January 27, 2006).

• More than 40% of Marriott International managers work their way up through the

ranks (Fortune, January 20, 2003).

• The New York Yankees have the highest payroll in major league baseball. In 2005, the

•

team payroll was $208,306,817, with a median of $5,833,334 per player (USA Today

Salary Database, February 2006).

The Dow Jones Industrial Average closed at 13,265 (Barron’s, May 5, 2007).

The numerical facts in the preceding statements ($222,600; $2.5 million; 31%; 26%;

$4300; 40%; $5,833,334; and 13,265) are called statistics. In this usage, the term statistics

refers to numerical facts such as averages, medians, percents, and index numbers that help

us understand a variety of business and economic conditions. However, as you will see, the

field, or subject, of statistics involves much more than numerical facts. In a broader sense,

statistics is defined as the art and science of collecting, analyzing, presenting, and interpreting data. Particularly in business and economics, the information provided by collecting, analyzing, presenting, and interpreting data gives managers and decision makers a

better understanding of the business and economic environment and thus enables them to

make more informed and better decisions. In this text, we emphasize the use of statistics

for business and economic decision making.

Chapter 1 begins with some illustrations of the applications of statistics in business and

economics. In Section 1.2 we define the term data and introduce the concept of a data set.

This section also introduces key terms such as variables and observations, discusses the

difference between quantitative and qualitative data, and illustrates the uses of crosssectional and time series data. Section 1.3 discusses how data can be obtained from existing sources or through surveys and experimental studies designed to obtain new data. The

important role that the Internet now plays in obtaining data is also highlighted. The uses of

data in developing descriptive statistics and in making statistical inferences are described

in Sections 1.4 and 1.5.

1.1

Applications in Business and Economics

In today’s global business and economic environment, anyone can access vast amounts of

statistical information. The most successful managers and decision makers understand the

information and know how to use it effectively. In this section, we provide examples that

illustrate some of the uses of statistics in business and economics.

Accounting

Public accounting firms use statistical sampling procedures when conducting audits for

their clients. For instance, suppose an accounting firm wants to determine whether the

amount of accounts receivable shown on a client’s balance sheet fairly represents the actual amount of accounts receivable. Usually the large number of individual accounts receivable makes reviewing and validating every account too time-consuming and expensive.

As common practice in such situations, the audit staff selects a subset of the accounts

called a sample. After reviewing the accuracy of the sampled accounts, the auditors draw a

conclusion as to whether the accounts receivable amount shown on the client’s balance

sheet is acceptable.

4

Chapter 1

Data and Statistics

Finance

Financial analysts use a variety of statistical information to guide their investment recommendations. In the case of stocks, the analysts review a variety of financial data including

price/earnings ratios and dividend yields. By comparing the information for an individual

stock with information about the stock market averages, a financial analyst can begin to

draw a conclusion as to whether an individual stock is over- or underpriced. For example,

Barron’s (September 12, 2005) reported that the average price/earnings ratio for the 30 stocks

in the Dow Jones Industrial Average was 16.5. JPMorgan showed a price/earnings ratio of

11.8. In this case, the statistical information on price/earnings ratios indicated a lower price

in comparison to earnings for JPMorgan than the average for the Dow Jones stocks. Therefore, a financial analyst might conclude that JPMorgan was underpriced. This and other

information about JPMorgan would help the analyst make a buy, sell, or hold recommendation for the stock.

Marketing

Electronic scanners at retail checkout counters collect data for a variety of marketing research applications. For example, data suppliers such as ACNielsen and Information Resources, Inc., purchase point-of-sale scanner data from grocery stores, process the data, and

then sell statistical summaries of the data to manufacturers. Manufacturers spend hundreds

of thousands of dollars per product category to obtain this type of scanner data. Manufacturers also purchase data and statistical summaries on promotional activities such as special pricing and the use of in-store displays. Brand managers can review the scanner

statistics and the promotional activity statistics to gain a better understanding of the relationship between promotional activities and sales. Such analyses often prove helpful in

establishing future marketing strategies for the various products.

Production

Today’s emphasis on quality makes quality control an important application of statistics

in production. A variety of statistical quality control charts are used to monitor the output of a production process. In particular, an x-bar chart can be used to monitor the average

output. Suppose, for example, that a machine fills containers with 12 ounces of a soft drink.

Periodically, a production worker selects a sample of containers and computes the average

number of ounces in the sample. This average, or x-bar value, is plotted on an x-bar chart. A

plotted value above the chart’s upper control limit indicates overfilling, and a plotted value

below the chart’s lower control limit indicates underfilling. The process is termed “in control” and allowed to continue as long as the plotted x-bar values fall between the chart’s

upper and lower control limits. Properly interpreted, an x-bar chart can help determine when

adjustments are necessary to correct a production process.

Economics

Economists frequently provide forecasts about the future of the economy or some aspect of

it. They use a variety of statistical information in making such forecasts. For instance, in

forecasting inflation rates, economists use statistical information on such indicators as

the Producer Price Index, the unemployment rate, and manufacturing capacity utilization.

Often these statistical indicators are entered into computerized forecasting models that

predict inflation rates.

1.2

5

Data

Applications of statistics such as those described in this section are an integral part of

this text. Such examples provide an overview of the breadth of statistical applications. To

supplement these examples, practitioners in the fields of business and economics provided

chapter-opening Statistics in Practice articles that introduce the material covered in each

chapter. The Statistics in Practice applications show the importance of statistics in a wide

variety of business and economic situations.

1.2

Data

Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation. All the data collected in a particular study are referred to as the data set for the

study. Table 1.1 shows a data set containing information for 25 companies that are part of

the S&P 500. The S&P 500 is made up of 500 companies selected by Standard & Poor’s.

These companies account for 76% of the market capitalization of all U.S. stocks. S&P 500

stocks are closely followed by investors and Wall Street analysts.

TABLE 1.1

DATA SET FOR 25 S&P 500 COMPANIES

Company

CD

file

BWS&P

Abbott Laboratories

Altria Group

Apollo Group

Bank of New York

Bristol-Myers Squibb

Cincinnati Financial

Comcast

Deere

eBay

Federated Dept. Stores

Hasbro

IBM

International Paper

Knight-Ridder

Manor Care

Medtronic

National Semiconductor

Novellus Systems

Pitney Bowes

Pulte Homes

SBC Communications

St. Paul Travelers

Teradyne

UnitedHealth Group

Wells Fargo

Exchange

Ticker

BusinessWeek

Rank

Share

Price

($)

N

N

NQ

N

N

NQ

NQ

N

NQ

N

N

N

N

N

N

N

N

NQ

N

N

N

N

N

N

N

ABT

MO

APOL

BK

BMY

CINF

CMCSA

DE

EBAY

FD

HAS

IBM

IP

KRI

HCR

MDT

NSM

NVLS

PBI

PHM

SBC

STA

TER

UNH

WFC

90

148

174

305

346

161

296

36

19

353

373

216

370

397

285

53

155

386

339

12

371

264

412

5

159

46

66

74

30

26

45

32

71

43

56

21

93

37

66

34

52

20

30

46

78

24

38

15

91

59

Source: BusinessWeek (April 4, 2005).

Earnings

per

Share

($)

2.02

4.57

0.90

1.85

1.21

2.73

0.43

5.77

0.57

3.86

0.96

4.94

0.98

4.13

1.90

1.79

1.03

1.06

2.05

7.67

1.52

1.53

0.84

3.94

4.09

6

Chapter 1

Data and Statistics

Elements, Variables, and Observations

Elements are the entities on which data are collected. For the data set in Table 1.1, each individual company’s stock is an element; the element names appear in the first column. With

25 stocks, the data set contains 25 elements.

A variable is a characteristic of interest for the elements. The data set in Table 1.1

includes the following five variables:

• Exchange: Where the stock is traded— N (New York Stock Exchange) and

•

•

•

•

NQ

(Nasdaq National Market)

Ticker Symbol: The abbreviation used to identify the stock on the exchange

listing

BusinessWeek Rank: A number from 1 to 500 that is a measure of company strength

Share Price ($): The closing price (February 28, 2005)

Earnings per Share ($): The earnings per share for the most recent 12 months

Measurements collected on each variable for every element in a study provide the data.

The set of measurements obtained for a particular element is called an observation. Referring to Table 1.1, we see that the set of measurements for the first observation (Abbott Laboratories) is N, ABT, 90, 46, and 2.02. The set of measurements for the second observation

(Altria Group) is N, MO, 148, 66, and 4.57, and so on. A data set with 25 elements contains

25 observations.

Scales of Measurement

Data collection requires one of the following scales of measurement: nominal, ordinal,

interval, or ratio. The scale of measurement determines the amount of information contained in the data and indicates the most appropriate data summarization and statistical

analyses.

When the data for a variable consist of labels or names used to identify an attribute of

the element, the scale of measurement is considered a nominal scale. For example, referring to the data in Table 1.1, we see that the scale of measurement for the exchange variable

is nominal because N and NQ are labels used to identify where the company’s stock is traded.

In cases where the scale of measurement is nominal, a numeric code as well as nonnumeric

labels may be used. For example, to facilitate data collection and to prepare the data for

entry into a computer database, we might use a numeric code by letting 1 denote the New

York Stock Exchange and 2 denote the Nasdaq National Market. In this case the numeric

values 1 and 2 provide the labels used to identify where the stock is traded. The scale of measurement is nominal even though the data appear as numeric values.

The scale of measurement for a variable is called an ordinal scale if the data exhibit the properties of nominal data and the order or rank of the data is meaningful. For

example, Eastside Automotive sends customers a questionnaire designed to obtain data

on the quality of its automotive repair service. Each customer provides a repair service

rating of excellent, good, or poor. Because the data obtained are the labels—excellent,

good, or poor—the data have the properties of nominal data. In addition, the data can be

ranked, or ordered, with respect to the service quality. Data recorded as excellent indicate the best service, followed by good and then poor. Thus, the scale of measurement

is ordinal. Note that the ordinal data can also be recorded using a numeric code. For

example, the BusinessWeek rank for the data in Table 1.1 is ordinal data. It provides a rank

from 1 to 500 based on BusinessWeek’s assessment of the company’s strength.

The scale of measurement for a variable becomes an interval scale if the data show the

properties of ordinal data and the interval between values is expressed in terms of a fixed

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