fourth edition

Ronald M. WeiersEberly College of Business andInformation TechnologyIndiana University of Pennsylvania

DUXBURY

THOMSON LEARNING

Australia • Canada * Mexico • SingaporeSpain • United Kingdom • United States

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A Preview of Business Statistics 1

Visual Descriptions of Data 17

Statistical Descriptions of Data 71

Data Collection and Sampling Methods

Probability: Review of Basic Concepts119

157

197239

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions 281

Estimation from Sample Data 307

Hypothesis Tests Involving a Sample Mean

or Proportion 351

Hypothesis Tests Involving Two Sample Means

or Proportions 407

Analysis of Variance Tests 457

Chi-Square Applications 517

Nonparametric Methods 563

Simple Linear Regression and Correlation 609

Multiple Regression and Correlation 659

Model Building 707

Models for Time Series and Forecasting 751

Decision Theory 811

Total Quality Management 839

BRIEF CONTENTS

\ \ j/ u /V

PART ONE

Business Statistics: Introduction and BackgroundA Preview of Business Statistics

1 1.1 Introduction 2Timely Topic, Tattered Image 2

What Is Business Statistics? 2

For the Consumer as Well as the Practitioner 3

PRACTITIONER PERSPECTIVE:

Describing Tourism at Niagara Falls 3

1.2 Statistics: Yesterday and Today 4Yesterday 4

Today 5

1.3 Descriptive versus Inferential StatisticsDescriptive Statistics 6

Inferential Statistics 6

1.4 Types of Variables and Scales of MeasurementQualitative Variables 9

Quantitative Variables 9

Scales of Measurement 10

1.5 Statistics in Business Decisions 12

1.6 Business Statistics: Tools versus Tricks

STATISTICS IN ACTION 1.1:

High Stakes on the Interstate: Car Phones and Accidents 14

1.7 Summary 14

13

CONTENTS Vll

Visual Description of Data 17

2.1 Introduction 18

2.2 The Data Array and the Frequency Distribution 18The Data Array 20

PRACTITIONER PERSPECTIVE:

Scoring Visual Points with InFocus 20

The Frequency Distribution 22

2.3 The Stem-and-Leaf Display and the Dotplot 29The Stem-and-Leaf Display 30

The Dotplot 32

2.4 Visual Representation of the Data 34Popular Graphical Methods 34

The Abuse of Visual Displays 44

STATISTICS IN ACTION 2.1 :

These Words Are Better Than a Ninth of a Picture 46

2.5 The Scatter Diagram 48

2.6 Tabulation, Contingency Tables,and the Excel PivotTable Wizard 54Simple Tabulation 54

Cross-Tabulation (Contingency Table) 54

2.7 Summary 60

Statistical Description of Data 71

3.1 Introduction 72

PRACTITIONER PERSPECTIVE:

Statistical Descriptors and the Bureau of the Census 73

3.2 Statistical Description: Measures of Central Tendency 74The Arithmetic Mean 74

The Weighted Mean 76

The Median 76

STATISTICS IN ACTION 3.1:

The United States, a People of Means 77

The Mode 78

Distribution Shape and Measures of Central Tendency 78

STATISTICS IN ACTION 3.2:

U.S. Males Post Skewed Incomes -80

3.3 Statistical Description: Measures of Dispersion 83Range 84

Quantiles 86

viii CONTENTS

Mean Absolute Deviation (MAD) 87

Variance and Standard Deviation 88

3.4 Additional Dispersion Topics 93The Box-and-Whisker Plot 93

Chebyshev's Theorem 95

The Empirical Rule 96

Standardized Data 96

The Coefficient of Variation 99

3.5 Descriptive Statistics from Grouped Data 101Arithmetic Mean from Grouped Data 102

Variance and Standard Deviation from Grouped Data 103

3.6 Statistical Measures of Association 104A Closing Note 107

STATISTICS IN ACTION 3.3:

The Consumer Price Index 108

3.7 Summary 109

Data Collection and Sampling Methods 119

4.1 Introduction 120

4.2 Research Basics 121Types of Studies 121

PRACTITIONER PERSPECTIVE:Data Collection with The Archimedes Group 122

The Research Process 123

Primary versus Secondary Data 123

4.3 Survey Research 124Types of Surveys 124

Questionnaire Design 124

Sampling Considerations in Survey Research 126

Errors in Survey Research 127

4.4 Experimentation and Observational Research 128Experimentation 128

Observational Research 130

4.5 Secondary Data 131Internal Sources 131

External Sources 132

Data Warehousing and Data Mining 133

Internet Data Sources 134

Evaluating Secondary Data 135

STATISTICS IN ACTION 4 .1 :

The Optimistic Homebuilders 136

CONTENTS ix

4.6 The Basics of Sampling 137Selected Terms 137

Why a Sample Instead of a Census? 137

4.7 Sampling Methods 139Probability Sampling 139

Nonprobability Sampling 146

STATISTICS IN ACTION 4.2:

Shopping for Jurors 147

STATISTICS IN ACTION 4.3:

A Sample of Sampling by Giving Away Samples 148

4.8 Summary 149

PART TWO

ProbabilityProbability; Review of Basic Concepts

158

157

5.1 Introduction

PRACTITIONER PERSPECTIVE:

Probabilities and Insurance with Good and Associates 159

5.2 Probability: Terms and ApproachesBasic Terms 160

The Classical Approach 161

The Relative Frequency Approach 161

The Subjective Approach 162

STATISTICS IN ACTION 5.1 :Relative Frequencies and Travel Safety 163

Probabilities and "Odds" 164

160

165

169

172

5.3 Unions and Intersections of Events

5.4 Addition Rules for ProbabilityWhen Events Are Mutually Exclusive 169

When Events Are Not Mutually Exclusive 170

5.5 Multiplication Rules for ProbabilityWhen Events Are Independent 173

When Events Are Not Independent 173

5.6 Bayes' Theorem and the Revision of Probabilities

5.7 Counting: Permutations and Combinations 183Fundamentals of Counting 183

STATISTICS IN ACTION 5.2:

Computer Assistance in the Name Game 184

177

CONTENTS

Permutations 185

Combinations 186

5.8 Summary 187

Discrete Probability Distributions 197

6.1 Introduction 198Random Variables: Discrete versus Continuous 199

PRACTITIONER PERSPECTIVE:

Saving Lives and Examining Data with Citizens' Ambulance 199

The Nature of a Discrete Probability Distribution 200

The Mean and Variance of a Discrete Probability Distribution 203

STATISTICS IN ACTION 6.1:

The Discrete Distribution That Took a Day Off 205

6.2 The Binomial Distribution 207Description and Applications 207

Using the Binomial Tables 211

Additional Comments on the Binomial Distribution 215

6.3 The Poisson Distribution 219Description and Applications 219

STATISTICS IN ACTION 6.2:Football Injuries and the Poisson Distribution 220

Using the Poisson Tables 222

The Poisson Approximation to the Binomial Distribution 225

6.4 Simulating Observations from aDiscrete Probability Distribution 227

6.5 Summary 231

Continuous Probability Distributions : 239

7.1 Introduction 240

PRACTITIONER PERSPECTIVE:

Navigating Normal Curves with Thorndike Sports Equipment 241

7.2 The Normal Distribution 242Description and Applications 242

Areas Beneath the Normal Curve 243

7.3 The Standard Normal Distribution 246Description and Applications 246

Using the Standard Normal Distribution Table 247

STATISTICS IN ACTION 7.1:

SAT Math Scores and the Normal Distribution 248

CONTENTS xi

7.4 The Normal Approximation tothe Binomial Distribution 258The Binomial Distribution: A Brief Review 258

The Mean and Standard Deviation 259

Correction for Continuity 259

The Approximation Procedure 260

7.5 The Exponential Distribution 264Description and Applications 264

Examples 265

7.6 Simulating Observations from aContinuous Probability Distribution 270

7.7 Summary 272

PART THREE

Sampling Distributions and EstimationSampling Distributions 281

8 8.1

8.2

8.3

8.4

8.5

8.6

8.7

Introduction 282

A Preview of Sampling Distributions

The Sampling Distribution of the MeanWhen the Population Is Normally Distributed 285

When the Populations Is Not Normally Distributed 288

283

285

The Sampling Distribution of the Proportion 291

Sampling Distributions When the Population Is Finite 294

Computer Simulation of Sampling Distributions 296

Summary 300

Estimation from Sample DataIntroduction

307.9 9.1 Introduction 308

PRACTITIONER PERSPECTIVE:

Estimation Relies on Sound Sampling Frame at Survey Sampling, Inc. 309

9.2 Point Estimates 310

9.3 A Preview of Interval Estimates 311

9.4 Confidence Interval Estimates for the Mean: a Known

9.5 Confidence Interval Estimates for the Mean: a- UnknownThe Student's t Distribution 319Confidence Intervals Using the f Distribution 322

314

319

xn CONTENTS

9.6 Confidence Interval Estimatesfor the Population Proportion 327

9.7 Sample Size Determination 331Estimating the Population Mean 332

Estimating the Population Proportion 333

STATISTICS IN ACTION 9.1:

Sampling Error in Survey Research 336

9.8 When the Population Is Finite 338Confidence-Interval Estimation 338

Sample Size Determination 339

9.9 Summary 342

PART FOUR

Hypothesis TestingHypothesis Tests Involving a Sample Mean or Proportion 351

.10 10.1 Introduction 352Null and Alternative Hypotheses 353

PRACTITIONER PERSPECTIVE:

Products Are Tested Extensively Before Receiving the Underwriters Laboratories Mark 353

Directional and Nondirectional Testing 354

Hypothesis Testing and the Nature of the Test 354

Errors in Hypothesis Testing 356

10.2 Hypothesis Testing: Basic Procedures 358

10.3 Testing a Mean, PopulationStandard Deviation Known 361Two-Tail Testing of a Mean, a Known 361

One-Tail Testing of a Mean, a Known 363

The p-value Approach to Hypothesis Testing 365

Computer-Assisted Hypothesis Tests and p-values 367

10.4 Confidence Intervals and Hypothesis Testing 371

10.5 Testing a Mean, PopulationStandard Deviation Unknown 372Two-Tail Testing of a Mean, a Unknown 373

One-Tail Testing of a Mean, cr Unknown 374

10.6 Testing a Proportion 381Two-Tail Testing of a Proportion 382

One-Tail Testing of a Proportion 383

CONTENTS xm

10.7 The Power of a Hypothesis Test 389Hypothesis Testing Errors and the Power of a Test 389

The Power of a Test: An Example 390

The Power Curve for a Hypothesis Test 391

The Effect of Increased Sample Size on Type I and Type II Errors 394

10.8 Summary 398

Hypothesis Tests Involving Two Sample Means or Proportions 407

11.1 Introduction 408.11PRACTITIONER PERSPECTIVE:

Comparing Sample Means and Proportions at Eddie Bauer 409

11.2 The Pooled-Variances t-Test for Comparingthe Means of Two Independent Samples 411

11.3 The Unequal-Variances t-Test for Comparingthe Means of Two Independent Samples 418

11.4 The z-Test for Comparing the Meansof Two Independent Samples 424

11.5 Comparing Two Means Whenthe Samples Are Dependent 429

11.6 Comparing Two Sample Proportions 435

STATISTICS IN ACTION 11.1:Looking for Mechanical Predators 438

11.7 Comparing the Variances ofTwo Independent Samples 442

11.8 Summary 447

Analysis of Variance Tests 457

12.1 Introduction 458.1212.2 Analysis of Variance: Basic Concepts 458

Analysis of Variance and Experimentation 458

PRACTITIONER PERSPECTIVE:

Main and Interaction Effects Are Important at Intel 459

Variation Between and Within the Groups 461

12.3 One-Way Analysis of Variance 463Purpose 463 '

Model and Assumptions 463

Procedure 464

Treatment Sum of Squares, SSTR 468

Error Sum of Squares, SSE 468

xiv CONTENTS

Total Sum of Squares, SST 4G8

Treatment Mean Square (MSTR) and Error Mean Square (MSE) 469

The Test Statistic, F 469

The Critical Value of Fand the Decision 469

Computer Outputs and Interpretation 471

One-Way ANOVA and the Pooled-Variances f-Test 473

12.4 The Randomized Block Design 479Purpose 479

Model and Assumptions 480

Procedure 481

Treatment Sum of Squares, SSTR 484

Block Sum of Squares, SSB 484

Total Sum of Squares, SST 485

Error Sum of Squares, SSE 485

Treatment Mean Square {MSTR) and Error Mean Square (MSE) 485

The Test Statistic, F 485

The Critical Value of Fand the Decision 486

Testing the Effectiveness of the Blocking Variable 487

Computer Outputs and Interpretation 488

Randomized Block ANOVA and the Dependent-Samples t-Test 488

12.5 Two-Way Analysis of Variance 493Purpose 493

Model and Assumptions 493

Procedure 495

Factor A Sum of Squares, SSA 498

Factor B Sum of Squares, SSB 499

Error Sum of Squares, SSE 500

Total Sum of Squares, SS7"5O0

Interaction Sum of Squares, SSAB 500

The Mean Square Terms 501

Computer Outputs and Interpretation 503

12.6 Summary 509

Chi-Square Applications 517

.13 13.1 Introduction 518

13.2 Basic Concepts in Chi-Square Testing 518The Chi-Square Distribution 518

PRACTITIONER PERSPECTIVE:

Using Chi-Square Tests at Walker Information 519

An Overview of the Chi-Square Tests 520

13.3 Tests for Goodness of Fit and Normality 523Purpose 523

Procedure 523

CONTENTS xv

13.4 Testing the Independence of Two Variables 534Purpose 534

Procedure 534

STATISTICS IN ACTION 13.1:

Network Popularity Comparison 538

13.5 Comparing Proportions from k Independent Samples 541Purpose 541

Procedure 542

13.6 Estimation and Tests Regardingthe Population Variance 546The Confidence Interval for a Population Variance 546

Hypothesis Tests for the Population Variance 549

13.7 Summary 552

Nonparametric Methods 563

.14 14.1 Introduction 564Nonparametric Testing 564

Advantages and Disadvantages of Nonparametric Testing 565

14.2 Wilcoxon Signed Rank Test for One Sample 566Description and Applications 566

The Normal Approximation 569

14.3 Wilcoxon Signed Rank Test forComparing Paired Samples 571Description and Applications 571

14.4 Wilcoxon Rank Rum Test forComparing Two Independent Samples 575Description and Applications 575

The Normal Approximation 577

14.5 Kruskal-Wallis Test for ComparingMore Than Two Independent Samples 579Description and Applications 579

14.6 Friedman Test for the Randomized Block Design 583Description and Applications 583

14.7 Other Nonparametric Methods 588Sign Test for Comparing Paired Samples 588

The Runs Test for Randomness 593

Lilliefors Test for Normality 595

14.8 Summary 601

xvi CONTENTS

PART FIVE

Regression, Model Building, and Time SeriesSimple Linear Regression and Correlation

Introduction

609

.15 15.1 610

PRACTITIONER PERSPECTIVE:

Statistics and Regression Analysis with Duxbury/Thomson Learning 611

15.2

15.3

15.4

15.5

The Simple Linear Regression Model 612Model and Assumptions 612

The Least-Squares Criterion 613

Determining the Least-Squares Regression Line 614

Point Estimates Using the Regression Line 615

Interval Estimation Using the Sample Regression LineThe Standard Error of Estimate 620

Confidence Interval for the Mean of /Given a Specific xValue 621

Prediction Interval for an Individual /Observation 622

Correlation Analysis 626The Coefficient of Correlation 627

The Coefficient of Determination 627

619

Estimation and Tests Regardingthe Sample Regression LineTesting the Coefficient of Correlation 631

Testing and Estimation for the Slope 632

631

STATISTICS IN ACTION 15.1:

The Beta Coefficient and Investment Decisions 633

The Analysis of Variance Perspective 634

15.6 Additional Topics in Regressionand Correlation Analysis 637Residual Analysis 637

Cautionary Notes 642

STATISTICS IN ACTION 15.2:

Major League Baseball: Does Money Really Win Games? 644

15.7 Summary 646

Multiple Regression and Correlation

Introduction ;

659

.16 16.1 660

PRACTITIONER PERSPECTIVE:

Multiple Regression with the NCAA 661

16.2 The Multiple Regression ModelModel and Assumptions 662

662

CONTENTS xvii

Determining the Sample Regression Equation GG3

Interpreting the Regression Equation 665

Point Estimates Using the Regression Equation 666

16.3 Interval Estimation in Multiple Regression 669The Multiple Standard Error of Estimate 670

Confidence Interval for the Conditional Mean of y 671

Prediction Interval for an Individual /Observation 672

16.4 Multiple Correlation Analysis 675The Coefficient of Multiple Determination 675

16.5 Significance Tests in Multiple Regressionand Correlation 678Testing the Significance of the Regression Equation 678

Testing the Partial Regression Coefficients 680

Interval Estimation for the Partial Regression Coefficients 681

16.6 Overview of the Computer Analysisand Interpretation 683A Summary of the Results 683

STATISTICS IN ACTION 16.1:

Predicting Holiday Traffic Fatalities 686

Residual Analysis 686

16.7 Additional Topics in Multiple Regressionand Correlation 693Including Qualitative Data: The Dummy Variable 693

Multicollinearity 695

16.8 Summary 697

Model Building 707

.17 17.1 Introduction 708

17.2 Polynomial Models with One QuantitativePredictor Variable 708The General Polynomial Model 710

PRACTITIONER PERSPECTIVE:

Model Building with Research International USA 710

First-Order Polynomial Model 711

Second-Order Polynomial Model 711

Third-Order Polynomial Model 712

17.3 Polynomial Models with Two QuantitativePredictor Variables 717First-Order Model with Two Variables 718

First-Order Model with an Interaction Term 718

Second-Order Model with Interaction 719

xviii CONTENTS

.18

17.4 Qualitative Variables 723Qualitative Variable Representing Two Possible Categories 724

Qualitative Variables Representing More Than Two Possible Categories 724

17.5 Data Transformations 728

17.6 Multicollinearity 731

17.7 Stepwise Regression 734

STATISTICS IN ACTION 17.1:

Stepwise Regression and the NFL Passer Rating 739

17.8 Selecting a Model 742

17.9 Summary 743

Models for Time Series and Forecasting 75118.1 Introduction 752

18.2 Time Series 752

PRACTITIONER PERSPECTIVE:

Retirees Depend on Cost-of-Living Adjustments to Fight Inflation 753

Components of a Time Series 754

STATISTICS IN ACTION 18.1:

Global Temperatures: A 100,000-Year Cycle 754

Fitting a Linear Trend Equation 756

Fitting a Quadratic Trend Equation 758

18.3 Smoothing Techniques 760The Moving Average 760

Exponential Smoothing 766

18.4 Seasonal Indexes 771The Ratio to Moving Average Method 772

Deseasonalizing the Time Series 774

18.5 Forecasting 777Forecasts Using the Trend Equation 778

Forecasting with Exponential Smoothing 778

Seasonal Indexes in Forecasting 779

18.6 Evaluating Alternative Models MAD and MSE 782

18.7 Autocorrelation, the Durbin-Watson Test,and Autoregressive Forecasting 785Autocorrelation and the Durbin-Watson Test 785

The Autoregressive Forecasting Model 789

18.8 Index Numbers 795The Consumer Price Index 796

CONTENTS xix

STATISTICS IN ACTION 18.2:

The CPI Time Machine 798

Other Indexes 798

Shifting the Base of an Index 799

18.9 Summary 800

PART SIX

Special TopicsDecision Theory 811

.19 19.1

19.2

Introduction 812

Structuring the Decision SituationAlternatives 813

813

PRACTITIONER PERSPECTIVE:

Making Decisions with CompAS Controls, Inc. 813

States of Nature 814

STATISTICS IN ACTION 19.1:

New Technology Makes Invention Hit Bottom 814

The Payoff Table 815

19.3 Non-Bayesian Decision Making 817Maximin 817

Maximax 817

Minimax Regret 818

19.4 Bayesian Decision Making 820Expected Payoff 821

The Expected Value of Perfect Information 822

STATISTICS IN ACTION 19.2:

Expected Payoff, Maximax, and the Lottery 823

19.5 The Opportunity Loss Approach 826

19.6 Incremental Analysis and Inventory Decisions

19.7 Summary 831

Appendix to Chapter 19:The Expected Value of Imperfect Information

827

833

Total Quality Management 839.20 20.1 840Introduction

What Is Quality? 840

PRACTITIONER PERSPECTIVE:

Practicing TQM at Ben ft Jerry's Homemade 841

xx CONTENTS

Why Is Quality Important? 842

Process Variation and Product Quality 843

20.2 A Historical Perspective and Defect Detection 844

20.3 The Emergence of Total Quality Management 845TQM Pioneers 846The Process Orientation 847

20.4 Practicing Total Quality Management 848"Kaizen" and TQM 848

Deming's 14 Points 848

The Quality Audit 849

Competitive Benchmarking 850

Just-in-Time Manufacturing 850

Worker Empowerment 851

STATISTICS IN ACTION 20.1:

Quality Circles and the "Suggestion Box" 852

Awards and the Recognition of Quality 852

20.5 Some Statistical Tools for Total Quality Management 853The Process Flow Chart 853

The Cause-and-Effect Diagram 853

The Pareto Diagram 855

The Check Sheet 855

Taguchi Methods 856

Designed Experiments 857

20.6 Statistical Process Control: The Concepts 858Types of Control Charts 858

The Control Chart Format 858

20.7 Control Charts for Variables 859Mean Charts 859

Construction of a Mean Chart 860

Range Charts 862

20.8 Control Charts for Attributes 868p-Charts 869

c-Charts 870

20.9 More on Computer-Assisted Statistical Process Control 877

20.10 Summary 879

Appendix A: Statistical Tables 887

Appendix B: Selected Answers 923

Index/Glossary 927

CONTENTS xxi