Statistics for business and economics

INTERNATIONAL STUDENT EDITION

S t a t is t ic s

f o r B u s in e s s

a n d E c o n o m ic s

Tenth Edition

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STATISTICS FOR

BUSINESS AND

ECONOMICS lOe

David R. Anderson

University of Cincinnati

Dennis J. Sweeney

University of Cincinnati

Thomas A. Williams

Rochester Institute of Technology

THOMSON

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SOUTH-WESTERN

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Statistics for B usiness and Econom ics, lOe

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Dedicated to

Marcia, Cherri, and Robbie

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Brief Contents

Preface xxi

About the Authors xxvii

Chapter 1 Data and Statistics 1

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 23

Chapter 3 Descriptive Statistics: Numerical Measures 76

Chapter 4 Introduction to Probability 139

Chapter 5 Discrete Probability Distributions 184

Chapter 6 Continuous Probability Distributions 223

Chapter 7 Sampling and Sampling Distributions 257

Chapter 8 Interval Estimation 297

Chapter 9 Hypothesis Testing 336

Chapter 10 Statistical Inference About Means and Proportions with

Two Populations 393

Chapter 11 Inferences About Population Variances 432

Chapter 12 Tests of Goodness of Fit and Independence 457

Chapter 13 Analysis of Variance and Experimental Design 490

Chapter 14 Simple Linear Regression 553

Chapter 15 M ultiple Regression 635

Chapter 16 Regression Analysis: Model Building 703

Chapter 17 Index Numbers 757

Chapter 18 Forecasting 778

Chapter 19 Nonparametric Methods 825

Chapter 20 Statistical Methods for Quality Control 859

Chapter 21 Decision Analysis 889

Chapter 22 Sample Survey On CD

Appendix A References and Bibliography 926

Appendix B Tables 928

Appendix C Summation Notation 957

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

Exercises 959

Index 1010

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Contents

3*

Preface xxi

About the Authors xxvii

Chapter 1 Data and Statistics 1

Statistics in Practice: Business Week 2

1.1 Applications in Business and Economics 3

Accounting 3

Finance 3

Marketing 4

Production 4

Economics 4

1.2 Data 5

Elements, Variables, and Observations 5

Scales of Measurement 6

Qualitative and Quantitative Data 7

Cross-Sectional and Time Series Data 7

1.3 Data Sources 8

Existing Sources 8

Statistical Studies 9

Data Acquisition Errors 12

1.4 Descriptive Statistics 12

1.5 Statistical Inference 14

1.6 Computers and Statistical Analysis 16

Summary 16

Glossary 16

Exercises 17

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 23

Statistics in Practice: Colgate-Palmolive Company 24

2.1 Summarizing Qualitative Data 25

Frequency Distribution 25

Relative Frequency and Percent Frequency Distributions 26

Bar Graphs and Pie Charts 26

2.2 Summarizing Quantitative Data 31

Frequency Distribution 31

Relative Frequency and Percent Frequency Distributions 32

Dot Plot 32 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

viii STATISTICS FOR BUSINESS AND ECONOMICS

Histogram 33

Cumulative Distributions 34

Ogive 36

2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 40

2.4 Crosstabulations and Scatter Diagrams 45

Crosstabulation 45

Simpson's Paradox 47

Scatter Diagram and Trendline 49

Summary 54

Glossary 56

Key Formulas 57

Supplementary Exercises 57

Case Problem Pelican Stores 63

Appendix 2.1 Using Minitab for Tabular and Graphical Presentations 64

Appendix 2.2 Using Excel for Tabular and Graphical Presentations 66

Chapter 3 Descriptive Statistics: Numerical Measures 76

Statistics in Practice: Small Fry Design 77

3.1 Measures of Location 78

Mean 78

Median 79

Mode 80

Percentiles 81

Quartiles 82

3.2 Measures of Variability 87

Range 87

Interquartile Range 88

Variance 88

Standard Deviation 90

Coefficient of Variation 91

3.3 Measures of Distribution Shape, Relative Location, and Detecting

Outliers 94

Distribution Shape 94

z-Scores 94

Chebyshev’s Theorem 96

Empirical Rule 97

Detecting Outliers 98

3.4 Exploratory Data Analysis 101

Five-Number Summary 101

Box Plot 102

3.5 Measures of Association Between Two Variables 105

Covariance 106

Interpretation of the Covariance 107

Correlation Coefficient 110

Interpretation of the Correlation Coefficient 111 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contents

3.6 The Weighted Mean and Working with Grouped Data 114

Weighted Mean 115

Grouped Data 116

Summary 120

Glossary 121

Key Formulas 122

Supplementary Exercises 124

Case Problem 1 Pelican Stores 129

Case Problem 2 National Health Care Association 130

Case Problem 3 Business Schools of Asia-Pacific 131

Appendix 3.1 Descriptive Statistics Using Minitab 133

Appendix 3.2 Descriptive Statistics Using Excel 135

Chapter 4 Introduction to Probability 139

Statistics in Practice: Morton International 140

4.1 Experiments, Counting Rules, and Assigning Probabilities 141

Counting Rules. Combinations, and Permutations 142

Assigning Probabilities 146

Probabilities for the KP&L Project 148

4.2 Events and Their Probabilities 151

4.3 Some Basic Relationships of Probability 155

Complement of an Event 155

Addition Law 156

4.4 Conditional Probability 161

Independent Events 165

Multiplication Law 165

4.5 Baves’ Theorem 169

Tabular Approach 173

Summary 175

Glossary 175

Key Formulas 176

Supplementary Exercises 177

Case Problem Hamilton County Judges 181

Chapter 5 Discrete Probability Distributions 184

Statistics in Practice: Citibank 185

5.1 Random Variables 185

Discrete Random Variables 186

Continuous Random Variables 187

5.2 Discrete Probability Distributions 188

5.3 Expected Value and Variance 194

Expected Value 194

Variance 194 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

STATISTICS FOR BUSINESS AND ECONOMICS

5.4 Binomial Probability Distribution 198

A Binomial Experiment 199

Martin Clothing Store Problem 200

Using Tables of Binomial Probabilities 204

Expected Value and Variance for the Binomial Distribution 205

5.5 Poisson Probability Distribution 208

An Example Involving Time Intervals 209

An Example Involving Length or Distance Intervals 211

5.6 Hypergeometric Probability Distribution 212

Summary 215

Glossary 216

Key Formulas 217

Supplementary Exercises 218

Appendix 5.1 Discrete Probability Distributions with Nlinitab 220

Appendix 5.2 Discrete Probability Distributions with Excel 221

Chapter 6 Continuous Probability Distributions 223

Statistics in Practice: Procter & Gamble 224

6.1 Uniform Probability Distribution 225

Area as a Measure of Probability 226

6.2 Normal Probability Distribution 229

Normal Curve 229

Standard Normal Probability Distribution 231

Computing Probabilities for Any Normal Distribution 237

Grear Tire Company Problem 238

6.3 Normal Approximation of Binomial Probabilities 243

6.4 Exponential Probability Distribution 246

Computing Probabilities for the Exponential Distribution 246

Relationship Betw een the Poisson and Exponential Distributions 248

Summary 250

Glossary 250

Key Formulas 250

Supplementary Exercises 251

Case Problem Specialty Toys 254

Appendix 6.1 Continuous Probability Distributions with Minitab 255

Appendix 6.2 Continuous Probability Distributions with Excel 256

Chapter 7 Sam pling and Sam pling Distributions 257

Statistics in Practice: MeadWestvaco Corporation 258

7.1 The Electronics Associates Sampling Problem 259

7.2 Simple Random Sampling 260

Sampling from a Finite Population 260

Sampling from an Infinite Population 261 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contents

7.3 Point Estimation 264

7.4 Introduction to Sampling Distributions 267

7.5 Sampling Distribution of x 270

Expected Value of .v 270

Standard Deviation of x 271

Form of the Sampling Distribution of x 272

Sampling Distribution of x for the EAI Problem 273

Practical Value of the Sampling Distribution of x T14

Relationship Between the Sample Size and the Sampling Distribution

of x 275

7.6 Sampling Distribution of p 279

Expected Value of p 280

Standard Deviation of p 280

Form of the Sampling Distribution of p 281

Practical Value of the Sampling Distribution of p 281

7.7 Properties of Point Estimators 284

Unbiased 285

Efficiency 286

Consistency 287

7.8 Other Sampling Methods 287

Stratified Random Sampling 287

Cluster Sampling 288

Systematic Sampling 288

Convenience Sampling 289

Judgment Sampling 289

Summary 290

Glossary 290

Key Formulas 291

Supplementary Exercises 292

Appendix 7.1 The Expected Value and Standard Deviation

of x 294

Appendix 7.2 Random Sampling with Minitab 295

Appendix 7.3 Random Sampling with Excel 296

Chapter 8 Interval Estimation 297

Statistics in Practice: Food Lion 298

8.1 Population Mean: a Known 299

Margin of Error and the Interval Estimate 300

Practical Advice 303

8.2 Population Mean: a Unknown 305

Margin of Error and the Interval Estimate 306

Practical Advice 309

Using a Small Sample 309

Summary of Interval Estimation Procedures 311

8.3 Determining the Sample Size 314 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

xii STATISTICS FOR BUSINESS AND ECONOMICS

8.4 Population Proportion 317

Determining the Sample Size 319

Summary 322

Glossary 323

Key Formulas 324

Supplementary Exercises 324

Case Problem 1 Bock Investment Services 327

Case Problem 2 Gulf Real Estate Properties 327

Case Problem 3 Metropolitan Research, Inc. 330

Appendix 8.1 Interval Estimation with Minitab 331

Appendix 8.2 Interval Estimation Using Excel 332

Chapter 9 Hypothesis Testing 336

Statistics in Practice: John Morrell & Company 337

9.1 Developing Null and Alternative Hypotheses 338

Testing Research Hypotheses 338

Testing the Validity of a Claim 338

Testing in Decision-Making Situations 339

Summary of Forms for Null and Alternative Hypotheses 339

9.2 Type I and Type II Errors 340

9.3 Population Mean: o Known 343

One-Tailed Test 343

Two-Tailed Test 349

Summary and Practical Advice 352

Relationship Between Interval Estimation and Hypothesis

Testing 353

9.4 Population Mean: a Unknown 358

One-Tailed Test 358

Two-Tailed Test 360

Summary and Practical Advice 361

9.5 Population Proportion 365

Summary 367

9.6 Hypothesis Testing and Decision Making 370

9.7 Calculating the Probability of Type II Errors 371

9.8 Determining the Sample Size for Hypothesis Test About

a Population Mean 376

Summary 380

Glossary 380

Key Formulas 381

Supplementary Exercises 381

Case Problem I Quality Associates, Inc. 384

Case Problem 2 Unemployment study 385

Appendix 9.1 Hypothesis Testing with Minitab 386

Appendix 9.2 Hypothesis Testing with Excel 388

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Contents

Chapter 10 Statistical Inference About Means and Proportions

with Two Populations 393

Statistics in Practice: Fisons Corporation 394

10.1 Inferences About the Difference Between Two Population Means:

<7, and <t2 Known 395

Interval Estimate o f/i, — ft2 395

Hypothesis Tests About//, - n 2 397

Practical Advice 399

10.2 Inferences About the Difference Between Two Population Means:

a , and a 2 Unknown 402

Interval Estimation of //, - u 2 402

Hypothesis Tests About u, - / / , 403

Practical Advice 405

10.3 Inferences About the Difference Between Two Population Means:

Matched Samples 411

10.4 Inferences About the Difference Between Two Population Proportions 417

Interval Estimation of p, — p 2 417

Hypothesis Tests About p, — p 2 419

Summary 422

Glossary 423

Key Formulas 423

Supplementary Exercises 425

Case Problem Par, Inc. 427

Appendix 10.1 Inferences About Two Populations Using Minitab 428

Appendix 10.2 Inferences About Two Populations Using Excel 430

Chapter 11 Inferences About Population Variances 432

Statistics in Practice: U.S. General Accounting Office 433

11.1 Inferences About a Population Variance 434

Interval Estimation 434

Hypothesis Testing 438

11.2 Inferences About Two Population Variances 443

Summary 450

Key Formulas 450

Supplementary Exercises 451

Case Problem Air Force Training Program 452

Appendix 11.1 Population Variances with Minitab 454

Appendix 11.2 Population Variances with Excel 455

Chapter 12 Tests of Goodness of Fit and Independence 457

Statistics in Practice: United Way 458

12.1 Goodness of Fit Test: A Multinomial Population 459

12.2 Test of Independence 464

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xiv STATISTICS FOR BUSINESS AND ECONOMICS

12.3 Goodness of Fit Test: Poisson and Normal Distributions 471

Poisson Distribution 472

Normal Distribution 475

Summary 481

Glossary 481

Key Formulas 481

Supplementary Exercises 482

Case Problem A Bipartisan Agenda for Change 485

Appendix 12.1 Tests of Goodness of Fit and Independence Using Minitab 486

Appendix 12.2 Tests of Goodness of Fit and Independence Using Excel 487

Chapter 13 Analysis of Variance and Experimental Design 490

Statistics in Practice: Burke Marketing Services, Inc. 491

13.1 An Introduction to Analysis of Variance 491

Assumptions for Analysis of Variance 493

A Conceptual Overview 493

13.2 Analysis of Variance: Testing for the Equality of k Population

Means 495

Between-Treatments Estimate of Population Variance 496

Within-Treatments Estimate of Population Variance 497

Comparing the Variance Estimates: The /■'Test 498

ANOVA Table 500

Computer Results for Analysis of Variance 500

13.3 Multiple Comparison Procedures 505

Fisher’s LSD 506

Type I Error Rates 508

13.4 An Introduction to Experimental Design 511

Data Collection 512

13.5 Completely Randomized Designs 513

Between-Treatments Estimate of Population Variance 514

Within-Treatments Estimate of Population Variance 514

Comparing the Variance Estimates: The FTest 514

ANOVA Table 515

Pairwise Comparisons 515

13.6 Randomized Block Design 519

Air Traffic Controller Stress Test 520

ANOVA Procedure 521

Computations and Conclusions 522

13.7 Factorial Experiments 526

ANOVA Procedure 527

Computations and Conclusions 528

Summary 534

Glossary 534

Key Formulas 535

Supplementary Exercises 537 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn

Contents xv

Case Problem 1 Wentworth Medical Center 545

Case Problem 2 Compensation for ID Professionals 546

Appendix 13.1 Analysis of Variance and Experimental Design with Minitab 547

Appendix 13.2 Analysis of Variance and Experimental Design with Excel 548

Chapter 14 Simple Linear Regression 553

Statistics in Practice: Alliance Data Systems 554

14.1 Simple Linear Regression Model 555

Regression Model and Regression Equation 555

Estimated Regression Equation 556

14.2 Least Squares Method 558

14.3 Coefficient of Determination 569

Correlation Coefficient 572

14.4 Model Assumptions 576

14.5 Testing for Significance 578

Estimate of a 2 578

I Test 579

Confidence Interval for fit 580

F Test 581

Some Cautions About the Interpretation of Significance Tests 583

14.6 Using the Estimated Regression Equation for Estimation and

Prediction 587

Point Estimation 587

Interval Estimation 587

Confidence Interval for the Mean Value of y 588

Prediction Interval for an Individual Value of y 589

14.7 Computer Solution 593

14.8 Residual Analysis: Validating Model Assumptions 598

Residual Plot Against .v 599

Residual Plot Against v 600

Standardized Residuals 600

Normal Probability Plot 603

14.9 Residual Analysis: Outliers and Influential Observations 607

Detecting Outliers 607

Detecting Influential Observations 609

Summary 614

Glossary 615

Key Formulas 616

Supplementary Exercises 618

Case Problem 1 Spending and Student Achievement 623

Case Problem 2 U.S. Department of Transportation 625

Case Problem 3 Alumni Giving 626

Case Problem 4 Major League Baseball Team Values 628

Appendix 14.1 Calculus-Based Derivation of Least Squares Formulas 629

Appendix 14.2 A Test for Significance Using Correlation 630

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xvi STATISTICS FOR BUSINESS AND ECONOMICS

Appendix 14.3 Regression Analysis with Minitab 631

Appendix 14.4 Regression Analysis with Excel 632

Chapter 15 M ultiple Regression 635

Statistics in Practice: International Paper 636

15.1 Multiple Regression Model 637

Regression Model and Regression Equation 637

Estimated Multiple Regression Equation 637

15.2 Least Squares Method 638

An Example: Butler Trucking Company 639

Note on Interpretation of Coefficients 641

15.3 Multiple Coefficient of Determination 646

15.4 Model Assumptions 649

15.5 Testing for Significance 650

F Test 651

t Test 654

Multicollinearity 654

15.6 Using the Estimated Regression Equation for Estimation and Prediction 658

15.7 Qualitative Independent Variables 660

An Example: Johnson Filtration. Inc. 660

Interpreting the Parameters 662

More Complex Qualitative Variables 664

15.8 Residual Analysis 668

Detecting Outliers 669

Studentized Deleted Residuals and Outliers 670

Influential Observations 671

Using Cook’s Distance Measure to Identify Influential Observations 671

15.9 Logistic Regression 675

Logistic Regression Equation 676

Estimating the Logistic Regression Equation 677

Testing for Significance 679

Managerial Use 680

Interpreting the Logistic Regression Equation 680

Logit Transformation 683

Summary 687

Glossary 687

Key Formulas 688

Supplementary Exercises 690

Case Problem 1 Consumer Research, Inc. 695

Case Problem 2 NFL Quarterback Rating 696

Case Problem 3 Predicting Student Proficiency Test Scores 698

Case Problem 4 Alumni Giving 699

Appendix 15.1 Multiple Regression with Minitab 699

Appendix 15.2 Multiple Regression with Excel 699

Appendix 15.3 Logistic Regression with Minitah 702 Số hóa bởi Trung tâm Học liệu – ĐH TN http://www.lrc-tnu.edu.vn