Introduction to Business Statistics

: 0.10 0.05 0.025 0.01 0.005

d.f. 1 3.078 6.314 12.706 31.821 63.657

2 1.886 2.920 4.303 6.965 9.925

3 1.638 2.353 3.182 4.541 5.841

4 1.533 2.132 2.776 3.747 4.604

5 1.476 2.015 2.571 3.365 4.032

6 1.440 1.943 2.447 3.143 3.707

7 1.415 1.895 2.365 2.998 3.499

8 1.397 1.860 2.306 2.896 3.355

9 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.169

11 1.363 1.796 2.201 2.718 3.106

12 1.356 1.782 2.179 2.681 3.055

13 1.350 1.771 2.160 2.650 3.012

14 1.345 1.761 2.145 2.624 2.977

15 1.341 1.753 2.131 2.602 2.947

16 1.337 1.746 2.120 2.583 2.921

17 1.333 1.740 2.110 2.567 2.898

18 1.330 1.734 2.101 2.552 2.878

19 1.328 1.729 2.093 2.539 2.861

20 1.325 1.725 2.086 2.528 2.845

21 1.323 1.721 2.080 2.518 2.831

22 1.321 1.717 2.074 2.508 2.819

23 1.319 1.714 2.069 2.500 2.807

24 1.318 1.711 2.064 2.492 2.797

25 1.316 1.708 2.060 2.485 2.787

26 1.315 1.706 2.056 2.479 2.779

27 1.314 1.703 2.052 2.473 2.771

28 1.313 1.701 2.048 2.467 2.763

29 1.311 1.699 2.045 2.462 2.756

30 1.310 1.697 2.042 2.457 2.750

31 1.309 1.696 2.040 2.453 2.744

32 1.309 1.694 2.037 2.449 2.738

33 1.308 1.692 2.035 2.445 2.733

34 1.307 1.691 2.032 2.441 2.728

35 1.306 1.690 2.030 2.438 2.724

36 1.306 1.688 2.028 2.435 2.719

37 1.305 1.687 2.026 2.431 2.715

38 1.304 1.686 2.024 2.429 2.712

39 1.304 1.685 2.023 2.426 2.708

40 1.303 1.684 2.021 2.423 2.704

41 1.303 1.683 2.020 2.421 2.701

42 1.302 1.682 2.018 2.418 2.698

43 1.302 1.681 2.017 2.416 2.695

44 1.301 1.680 2.015 2.414 2.692

45 1.301 1.679 2.014 2.412 2.690

The t-Distribution

0 t

a = right-tail area. (e.g., for

a right-tail area of 0.025 and

d.f. = 15, the t value is 2.131.)

Source: t-values generated by Minitab, then rounded to three decimal places.

: 0.10 0.05 0.025 0.01 0.005

d.f. 46 1.300 1.679 2.013 2.410 2.687

47 1.300 1.678 2.012 2.408 2.685

48 1.299 1.677 2.011 2.407 2.682

49 1.299 1.677 2.010 2.405 2.680

50 1.299 1.676 2.009 2.403 2.678

51 1.298 1.675 2.008 2.402 2.676

52 1.298 1.675 2.007 2.400 2.674

53 1.298 1.674 2.006 2.399 2.672

54 1.297 1.674 2.005 2.397 2.670

55 1.297 1.673 2.004 2.396 2.668

56 1.297 1.673 2.003 2.395 2.667

57 1.297 1.672 2.002 2.394 2.665

58 1.296 1.672 2.002 2.392 2.663

59 1.296 1.671 2.001 2.391 2.662

60 1.296 1.671 2.000 2.390 2.660

61 1.296 1.670 2.000 2.389 2.659

62 1.295 1.670 1.999 2.388 2.658

63 1.295 1.669 1.998 2.387 2.656

64 1.295 1.669 1.998 2.386 2.655

65 1.295 1.669 1.997 2.385 2.654

66 1.295 1.668 1.997 2.384 2.652

67 1.294 1.668 1.996 2.383 2.651

68 1.294 1.668 1.995 2.382 2.650

69 1.294 1.667 1.995 2.382 2.649

70 1.294 1.667 1.994 2.381 2.648

71 1.294 1.667 1.994 2.380 2.647

72 1.293 1.666 1.993 2.379 2.646

73 1.293 1.666 1.993 2.379 2.645

74 1.293 1.666 1.993 2.378 2.644

75 1.293 1.665 1.992 2.377 2.643

76 1.293 1.665 1.992 2.376 2.642

77 1.293 1.665 1.991 2.376 2.641

78 1.292 1.665 1.991 2.375 2.640

79 1.292 1.664 1.990 2.375 2.640

80 1.292 1.664 1.990 2.374 2.639

81 1.292 1.664 1.990 2.373 2.638

82 1.292 1.664 1.989 2.373 2.637

83 1.292 1.663 1.989 2.372 2.636

84 1.292 1.663 1.989 2.372 2.636

85 1.292 1.663 1.988 2.371 2.635

86 1.291 1.663 1.988 2.371 2.634

87 1.291 1.663 1.988 2.370 2.634

88 1.291 1.662 1.987 2.369 2.633

89 1.291 1.662 1.987 2.369 2.632

90 1.291 1.662 1.987 2.369 2.632

91 1.291 1.662 1.986 2.368 2.631

92 1.291 1.662 1.986 2.368 2.630

93 1.291 1.661 1.986 2.367 2.630

94 1.291 1.661 1.986 2.367 2.629

95 1.291 1.661 1.985 2.366 2.629

96 1.290 1.661 1.985 2.366 2.628

97 1.290 1.661 1.985 2.365 2.627

98 1.290 1.661 1.984 2.365 2.627

99 1.290 1.660 1.984 2.365 2.626

100 1.290 1.660 1.984 2.364 2.626

1.282 1.645 1.960 2.326 2.576

Computer Printouts and Instructions

Solutions for Excel and Minitab Page

Computer Printouts and Instructions

Solutions for Excel and Minitab Page

Visual Description

2.1 The Histogram 21

2.2 The Stem-And-Leaf Display* 26

2.3 The Dotplot 27

2.4 The Bar Chart 29

2.5 The Line Chart 30

2.6 The Pie Chart 32

2.7 The Scatter Diagram 40

2.8 The Cross-Tabulation 45

2.9 Cross-Tabulation with

Cell Summary Information 46

Statistical Description

3.1 Descriptive Statistics: Central

Tendency 65

3.2 Descriptive Statistics: Dispersion 75

3.3 The Box Plot* 77

3.4 Standardizing the Data 81

3.5 Coeffi cient of Correlation 88

Sampling

4.1 Simple Random Sampling 122

Discrete Probability Distributions

6.1 Binomial Probabilities 180

6.2 Hypergeometric Probabilities 185

6.3 Poisson Probabilities 191

6.4 Simulating Observations

From a Discrete Probability

Distribution 195

Continuous Probability Distributions

7.1 Normal Probabilities 219

7.2 Inverse Normal Probabilities 220

7.3 Exponential Probabilities 230

7.4 Inverse Exponential Probabilities 232

7.5 Simulating Observations From a

Continuous Probability Distribution 234

Sampling Distributions

8.1 Sampling Distributions and Computer

Simulation 260

Confi dence Intervals

9.1 Confi dence Interval For Population

Mean, Known* 279

9.2 Confi dence Interval For Population

Mean, Unknown* 286

9.3 Confi dence Interval For Population

Proportion* 290

9.4 Sample Size Determination 297

Hypothesis Tests: One Sample

10.1 Hypothesis Test For Population

Mean, Known* 326

10.2 Hypothesis Test For Population

Mean, Unknown* 335

10.3 Hypothesis Test For Population

Proportion* 342

10.4 The Power Curve For A Hypothesis Test 352

Hypothesis Tests: Comparing Two Samples

11.1 Pooled-Variances t-Test for (1  2),

Population Variances Unknown but

Assumed Equal 371

11.2 Unequal-Variances t-Test for (1  2),

Population Variances Unknown and

Not Equal 377

11.3 The z-Test for (1  2) 383

11.4 Comparing the Means of Dependent

Samples 388

11.5 The z-Test for Comparing Two

Sample Proportions* 393

11.6 Testing for the Equality of

Population Variances 399

Analysis of Variance

12.1 One-Way Analysis of Variance 424

12.2 Randomized Block Analysis of Variance 438

12.3 Two-Way Analysis of Variance 453

Chi-Square Applications

13.1 Chi-Square Test for Goodness of Fit 475

13.2 Chi-Square Goodness-of-Fit Test

for Normality* 477

13.3 Chi-Square Test for Independence of

Variables* 483

13.4 Chi-Square Test Comparing Proportions

From Independent Samples* 488

13.5 Confi dence Interval for a Population

Variance 494

13.6 Hypothesis Test for a Population

Variance 495

Nonparametric Methods

14.1 Wilcoxon Signed Rank Test for

One Sample* 512

14.2 Wilcoxon Signed Rank Test for

Comparing Paired Samples* 515

14.3 Wilcoxon Rank Sum Test for Two

Independent Samples* 520

14.4 Kruskal-Wallis Test for Comparing

More Than Two Independent Samples* 524

14.5 Friedman Test for the Randomized

Block Design* 529

14.6 Sign Test for Comparing Paired

Samples* 534

14.7 Runs Test for Randomness 538

14.8 Kolmogorov-Smirnov Test for Normality 541

14.9 Spearman Coeffi cient of Rank

Correlation* 543

Simple Linear Regression

15.1 Simple Linear Regression 558

Computer Printouts and Instructions

Solutions for Excel and Minitab Page

Seeing Statistics Applets

Computer Printouts and Instructions

Solutions for Excel and Minitab Page

15.2 Interval Estimation in Simple Linear

Regression* 565

15.3 Coeffi cient of Correlation 570

15.4 Residual Analysis 580

Multiple Regression

16.1 Multiple Regression 606

16.2 Interval Estimation in Multiple

Regression* 613

16.3 Residual Analysis in Multiple

Regression 627

Model Building

17.1 Fitting a Polynomial Regression

Equation, One Predictor Variable 649

17.2 Fitting a Polynomial Regression

Equation, Two Predictor Variables 656

17.3 Multiple Regression With Qualitative

Predictor Variables 661

17.4 Transformation of the Multiplicative

Model 665

17.5 The Correlation Matrix 668

17.6 Stepwise Regression* 671

Models for Time Series and Forecasting

18.1 Fitting a Linear or Quadratic Trend

Equation 691

18.2 Centered Moving Average For

Smoothing a Time Series 694

18.3 Excel Centered Moving Average Based

On Even Number of Periods 696

18.4 Exponentially Smoothing a Time Series 699

18.5 Determining Seasonal Indexes* 706

18.6 Forecasting With Exponential Smoothing 710

18.7 Durbin-Watson Test for Autocorrelation* 720

18.8 Autoregressive Forecasting 723

Statistical Process Control

20.1 Mean Chart* 780

20.2 Range Chart* 781

20.3 p-Chart* 789

20.4 c-Chart 792

Applet Title Text Section Applet Page

1 Infl uence of a Single Observation on the Median 3.2 99

2 Scatter Diagrams and Correlation 3.6 100

3 Sampling 4.6 132

4 Size and Shape of Normal Distribution 7.2 241

5 Normal Distribution Areas 7.3 242

6 Normal Approximation to Binomial Distribution 7.4 243

7 Distribution of Means—Fair Dice 8.3 268

8 Distribution of Means—Loaded Dice 8.3 269

9 Confi dence Interval Size 9.4 309

10 Comparing the Normal and Student t Distributions 9.5 310

11 Student t Distribution Areas 9.5 310

12 z-Interval and Hypothesis Testing 10.4 362

13 Statistical Power of a Test 10.7 363

14 Distribution of Difference Between Sample Means 11.4 410

15 F Distribution 12.3 464

16 Interaction Graph in Two-Way ANOVA 12.5 465

17 Chi-Square Distribution 13.2 504

18 Regression: Point Estimate for y 15.2 597

19 Point-Insertion Scatter Diagram and Correlation 15.4 598

20 Regression Error Components 15.4 599

21 Mean Control Chart 20.7 805

Key Item Location

Computer setup and notes Follows preface

t-table Precedes z-table

z-table Inside rear cover

Other printed tables Appendix A

Selected odd answers Appendix B

Seeing Statistics applets, Thorndike video units, case and exercise data sets,

Excel worksheet templates, and Data Analysis PlusTM 7.0 Excel add-in software

with accompanying workbooks, including Test Statistics and Estimators,

Online Chapter 21, appendices, and additional support http://www.cengage.com/bstatistics/weiers

* Data Analysis Plus™ 7.0 add-in

Ronald M. Weiers

Eberly College of Business and Information Technology

Indiana University of Pennsylvania

and

H. John Heinz III College

Carnegie Mellon University

WITH BUSINESS CASES BY

J. Brian Gray

University of Alabama

Lawrence H. Peters

Texas Christian University

BUSINESS STATISTICS

INTRODUCTION TO

7E

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Introduction to Business Statistics, Seventh

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Ronald M. Weiers

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v

Part 1: Business Statistics: Introduction and Background

1. A Preview of Business Statistics 1

2. Visual Description of Data 15

3. Statistical Description of Data 57

4. Data Collection and Sampling Methods 101

Part 2: Probability

5. Probability: Review of Basic Concepts 133

6. Discrete Probability Distributions 167

7. Continuous Probability Distributions 205

Part 3: Sampling Distributions and Estimation

8. Sampling Distributions 244

9. Estimation from Sample Data 270

Part 4: Hypothesis Testing

10. Hypothesis Tests Involving a Sample Mean or Proportion 311

11. Hypothesis Tests Involving Two Sample Means or Proportions 364

12. Analysis of Variance Tests 411

13. Chi-Square Applications 467

14. Nonparametric Methods 505

Part 5: Regression, Model Building, and Time Series

15. Simple Linear Regression and Correlation 551

16. Multiple Regression and Correlation 600

17. Model Building 644

18. Models for Time Series and Forecasting 687

Part 6: Special Topics

19. Decision Theory 737

20. Total Quality Management 758

21. Ethics in Statistical Analysis and Reporting (Online Chapter)

Appendices

A. Statistical Tables A-1

B. Selected Answers B-1

Index/Glossary I-1

BRIEF CONTENTS

vi

PART 1: BUSINESS STATISTICS: INTRODUCTION AND BACKGROUND

Chapter 1: A Preview of Business Statistics 1

1.1 Introduction 2

1.2 Statistics: Yesterday and Today 3

1.3 Descriptive Versus Inferential Statistics 5

1.4 Types of Variables and Scales of Measurement 8

1.5 Statistics in Business Decisions 11

1.6 Business Statistics: Tools Versus Tricks 11

1.7 Summary 12

Chapter 2: Visual Description of Data 15

2.1 Introduction 16

2.2 The Frequency Distribution and the Histogram 16

2.3 The Stem-and-Leaf Display and the Dotplot 24

2.4 Other Methods for Visual Representation of the Data 28

2.5 The Scatter Diagram 37

2.6 Tabulation, Contingency Tables, and the Excel PivotTable 42

2.7 Summary 48

Integrated Case: Thorndike Sports Equipment (Meet the Thorndikes:

See Video Unit One.) 53

Integrated Case: Springdale Shopping Survey 54

Chapter 3: Statistical Description of Data 57

3.1 Introduction 58

3.2 Statistical Description: Measures of Central Tendency 59

3.3 Statistical Description: Measures of Dispersion 67

3.4 Additional Dispersion Topics 77

3.5 Descriptive Statistics from Grouped Data 83

3.6 Statistical Measures of Association 86

3.7 Summary 90

Integrated Case: Thorndike Sports Equipment 96

Integrated Case: Springdale Shopping Survey 97

Business Case: Baldwin Computer Sales (A) 97

Seeing Statistics Applet 1: Influence of a Single Observation on the Median 99

Seeing Statistics Applet 2: Scatter Diagrams and Correlation 100

CONTENTS

Contents vii

Chapter 4: Data Collection and Sampling Methods 101

4.1 Introduction 102

4.2 Research Basics 102

4.3 Survey Research 105

4.4 Experimentation and Observational Research 109

4.5 Secondary Data 112

4.6 The Basics of Sampling 117

4.7 Sampling Methods 119

4.8 Summary 127

Integrated Case: Thorndike Sports Equipment—Video Unit Two 131

Seeing Statistics Applet 3: Sampling 132

PART 2: PROBABILITY

Chapter 5: Probability: Review of Basic Concepts 133

5.1 Introduction 134

5.2 Probability: Terms and Approaches 135

5.3 Unions and Intersections of Events 140

5.4 Addition Rules for Probability 143

5.5 Multiplication Rules for Probability 146

5.6 Bayes’ Theorem and the Revision of Probabilities 150

5.7 Counting: Permutations and Combinations 156

5.8 Summary 160

Integrated Case: Thorndike Sports Equipment 165

Integrated Case: Springdale Shopping Survey 166

Business Case: Baldwin Computer Sales (B) 166

Chapter 6: Discrete Probability Distributions 167

6.1 Introduction 168

6.2 The Binomial Distribution 175

6.3 The Hypergeometric Distribution 183

6.4 The Poisson Distribution 187

6.5 Simulating Observations from a Discrete Probability Distribution 194

6.6 Summary 199

Integrated Case: Thorndike Sports Equipment 203

Chapter 7: Continuous Probability Distributions 205

7.1 Introduction 206

7.2 The Normal Distribution 208

7.3 The Standard Normal Distribution 212

7.4 The Normal Approximation to the Binomial Distribution 223

7.5 The Exponential Distribution 228

viii Contents

7.6 Simulating Observations from a Continuous Probability Distribution 233

7.7 Summary 235

Integrated Case: Thorndike Sports Equipment

(Corresponds to Thorndike Video Unit Three) 240

Integrated Case: Thorndike Golf Products Division 240

Seeing Statistics Applet 4: Size and Shape of Normal Distribution 241

Seeing Statistics Applet 5: Normal Distribution Areas 242

Seeing Statistics Applet 6: Normal Approximation to Binomial Distribution 243

PART 3: SAMPLING DISTRIBUTIONS AND ESTIMATION

Chapter 8: Sampling Distributions 244

8.1 Introduction 245

8.2 A Preview of Sampling Distributions 245

8.3 The Sampling Distribution of the Mean 248

8.4 The Sampling Distribution of the Proportion 254

8.5 Sampling Distributions When the Population Is Finite 257

8.6 Computer Simulation of Sampling Distributions 259

8.7 Summary 262

Integrated Case: Thorndike Sports Equipment 266

Seeing Statistics Applet 7: Distribution of Means: Fair Dice 268

Seeing Statistics Applet 8: Distribution of Means: Loaded Dice 269

Chapter 9: Estimation from Sample Data 270

9.1 Introduction 271

9.2 Point Estimates 272

9.3 A Preview of Interval Estimates 273

9.4 Confidence Interval Estimates for the Mean: Known 276

9.5 Confidence Interval Estimates for the Mean: Unknown 281

9.6 Confidence Interval Estimates for the Population Proportion 288

9.7 Sample Size Determination 293

9.8 When the Population Is Finite 298

9.9 Summary 302

Integrated Case: Thorndike Sports Equipment (Thorndike Video Unit Four) 307

Integrated Case: Springdale Shopping Survey 308

Seeing Statistics Applet 9: Confidence Interval Size 309

Seeing Statistics Applet 10: Comparing the Normal and Student t Distributions 310

Seeing Statistics Applet 11: Student t Distribution Areas 310

PART 4: HYPOTHESIS TESTING

Chapter 10: Hypothesis Tests Involving a Sample Mean

or Proportion 311

10.1 Introduction 312

Contents ix

10.2 Hypothesis Testing: Basic Procedures 317

10.3 Testing a Mean, Population Standard Deviation Known 320

10.4 Confidence Intervals and Hypothesis Testing 329

10.5 Testing a Mean, Population Standard Deviation Unknown 330

10.6 Testing a Proportion 338

10.7 The Power of a Hypothesis Test 346

10.8 Summary 354

Integrated Case: Thorndike Sports Equipment 359

Integrated Case: Springdale Shopping Survey 360

Business Case: Pronto Pizza (A) 361

Seeing Statistics Applet 12: z-Interval and Hypothesis Testing 362

Seeing Statistics Applet 13: Statistical Power of a Test 363

Chapter 11: Hypothesis Tests Involving Two Sample

Means or Proportions 364

11.1 Introduction 365

11.2 The Pooled-Variances t-Test for Comparing the

Means of Two Independent Samples 366

11.3 The Unequal-Variances t-Test for Comparing the

Means of Two Independent Samples 374

11.4 The z-Test for Comparing the Means of Two

Independent Samples 380

11.5 Comparing Two Means When the Samples Are Dependent 385

11.6 Comparing Two Sample Proportions 391

11.7 Comparing the Variances of Two Independent Samples 397

11.8 Summary 401

Integrated Case: Thorndike Sports Equipment 407

Integrated Case: Springdale Shopping Survey 407

Business Case: Circuit Systems, Inc. (A) 408

Seeing Statistics Applet 14: Distribution of Difference Between Sample Means 410

Chapter 12: Analysis of Variance Tests 411

12.1 Introduction 412

12.2 Analysis of Variance: Basic Concepts 412

12.3 One-Way Analysis of Variance 416

12.4 The Randomized Block Design 429

12.5 Two-Way Analysis of Variance 441

12.6 Summary 457

Integrated Case: Thorndike Sports Equipment (Video Unit Six) 462

Integrated Case: Springdale Shopping Survey 462

Business Case: Fastest Courier in the West 463

Seeing Statistics Applet 15: F Distribution and ANOVA 464

Seeing Statistics Applet 16: Interaction Graph in Two-Way ANOVA 465

x Contents

Chapter 13: Chi-Square Applications 467

13.1 Introduction 468

13.2 Basic Concepts in Chi-Square Testing 468

13.3 Tests for Goodness of Fit and Normality 471

13.4 Testing the Independence of Two Variables 479

13.5 Comparing Proportions from k Independent Samples 486

13.6 Estimation and Tests Regarding the Population Variance 489

13.7 Summary 497

Integrated Case: Thorndike Sports Equipment 502

Integrated Case: Springdale Shopping Survey 503

Business Case: Baldwin Computer Sales (C) 503

Seeing Statistics Applet 17: Chi-Square Distribution 504

Chapter 14: Nonparametric Methods 505

14.1 Introduction 506

14.2 Wilcoxon Signed Rank Test for One Sample 508

14.3 Wilcoxon Signed Rank Test for Comparing Paired Samples 513

14.4 Wilcoxon Rank Sum Test for Comparing Two

Independent Samples 517

14.5 Kruskal-Wallis Test for Comparing More Than

Two Independent Samples 521

14.6 Friedman Test for the Randomized Block Design 525

14.7 Other Nonparametric Methods 530

14.8 Summary 545

Integrated Case: Thorndike Sports Equipment 549

Business Case: Circuit Systems, Inc. (B) 550

PART 5: REGRESSION, MODEL BUILDING, AND TIME SERIES

Chapter 15: Simple Linear Regression and Correlation 551

15.1 Introduction 552

15.2 The Simple Linear Regression Model 553

15.3 Interval Estimation Using the Sample Regression Line 561

15.4 Correlation Analysis 567

15.5 Estimation and Tests Regarding the Sample Regression Line 572

15.6 Additional Topics in Regression and Correlation Analysis 578

15.7 Summary 587

Integrated Case: Thorndike Sports Equipment 595

Integrated Case: Springdale Shopping Survey 596

Business Case: Pronto Pizza (B) 596

Seeing Statistics Applet 18: Regression: Point Estimate for y 597

Seeing Statistics Applet 19: Point Insertion Diagram and Correlation 598

Seeing Statistics Applet 20: Regression Error Components 599