**Introduction to Probability and Statistics, 15th Edition**

By William Mendenhall, Robert J. Beaver and Barbara M. Beaver

**Contents **

Introduction: What is Statistics? 1

The Population and the Sample 3

Descriptive and Inferential Statistics 4

Achieving the Objective of Inferential Statistics: The Necessary Steps 4

Keys for Successful Learning 5

DESCRIBING DATA WITH GRAPHS 7

1.1 Variables and Data 8

1.2 Types of Variables 9

1.3 Graphs for Categorical Data 11

Exercises 14

1.4 Graphs for Quantitative Data 17

Pie Charts and Bar Charts 17

Line Charts 19

Dotplots 20

Stem and Leaf Plots 20

Interpreting Graphs with a Critical Eye 22

1.5 Relative Frequency Histograms 24

Exercises 28

Chapter Review 33

Technology Today 33

Supplementary Exercises 42

CASE STUDY: How Is Your Blood Pressure? 49

DESCRIBING DATA WITH NUMERICAL MEASURES 50

2.1 Describing a Set of Data with Numerical Measures 51

2.2 Measures of Center 51

Exercises 55

2.3 Measures of Variability 57

Exercises 62

2.4 On the Practical Significance of the Standard Deviation 63

2.5 A Check on the Calculation of s 67

Exercises 69

2.6 Measures of Relative Standing 72

2.7 The Five-Number Summary and the Box Plot 77

Exercises 80

Chapter Review 83

Technology Today 84

Supplementary Exercises 87

CASE STUDY: The Boys of Summer 93

DESCRIBING BIVARIATE DATA 94

3.1 Bivariate Data 95

3.2 Graphs for Categorical Variables 95

Exercises 98

3.3 Scatterplots for Two Quantitative Variables 99

3.4 Numerical Measures for Quantitative Bivariate Data 101

Exercises 107

Chapter Review 109

Technology Today 109

Supplementary Exercises 114

CASE STUDY: Are Your Dishes Really Clean? 121

PROBABILITY AND PROBABILITY DISTRIBUTIONS 123

4.1 The Role of Probability in Statistics 124

4.2 Events and the Sample Space 124

4.3 Calculating Probabilities Using Simple Events 127

Exercises 130

4.4 Useful Counting Rules (Optional) 133

Exercises 137

4.5 Event Relations and Probability Rules 139

Calculating Probabilities for Unions and Complements 141

4.6 Independence, Conditional Probability, and

the Multiplication Rule 144

Exercises 149

4.7 Bayes’ Rule (Optional) 152

Exercises 156

4.8 Discrete Random Variables and Their Probability Distributions 158

Random Variables 158

Probability Distributions 158

The Mean and Standard Deviation for a Discrete Random Variable 160

Exercises 163

Chapter Review 166

Technology Today 167

Supplementary Exercises 169

CASE STUDY: Probability and Decision Making in the Congo 174

SEVERAL USEFUL DISCRETE DISTRIBUTIONS 175

5.1 Introduction 176

5.2 The Binomial Probability Distribution 176

Exercises 185

5.3 The Poisson Probability Distribution 188

Exercises 193

5.4 The Hypergeometric Probability Distribution 194

Exercises 196

Chapter Review 197

Technology Today 198

Supplementary Exercises 202

CASE STUDY: A Mystery: Cancers Near a Reactor 208

THE NORMAL PROBABILITY DISTRIBUTION 209

6.1 Probability Distributions for Continuous Random Variables 210

6.2 The Normal Probability Distribution 213

6.3 Tabulated Areas of the Normal Probability Distribution 214

The Standard Normal Random Variable 214

Calculating Probabilities for a General Normal Random Variable 218

Exercises 221

6.4 The Normal Approximation to the Binomial Probability

Distribution (Optional) 224

Exercises 229

Chapter Review 231

Technology Today 232

Supplementary Exercises 236

CASE STUDY: “Are You Going to Curve the Grades?” 241

SAMPLING DISTRIBUTIONS 242

7.1 Introduction 243

7.2 Sampling Plans and Experimental Designs 243

Exercises 246

7.3 Statistics and Sampling Distributions 248

7.4 The Central Limit Theorem 251

7.5 The Sampling Distribution of the Sample Mean 254

Standard Error 255

Exercises 258

7.6 The Sampling Distribution of the Sample Proportion 260

Exercises 264

7.7 A Sampling Application: Statistical Process Control (Optional) 266

A Control Chart for the Process Mean: The x_ Chart 267

A Control Chart for the Proportion Defective: The p Chart 269

Exercises 271

Chapter Review 272

Technology Today 273

Supplementary Exercises 276

CASE STUDY: Sampling the Roulette at Monte Carlo 279

LARGE-SAMPLE ESTIMATION 281

8.1 Where We’ve Been 282

8.2 Where We’re Going—Statistical Inference 282

8.3 Types of Estimators 283

8.4 Point Estimation 284

Exercises 289

8.5 Interval Estimation 291

Constructing a Confidence Interval 292

Large-Sample Confidence Interval for a Population Mean m 294

Interpreting the Confidence Interval 295

Large-Sample Confidence Interval for a Population Proportion p 297

Exercises 299

8.6 Estimating the Difference between Two Population Means 301

Exercises 304

8.7 Estimating the Difference between Two Binomial Proportions 307

Exercises 309

8.8 One-Sided Confidence Bounds 311

8.9 Choosing the Sample Size 312

Exercises 316

Chapter Review 318

Supplementary Exercises 318

CASE STUDY: How Reliable Is That Poll?

CBS News: How and Where America Eats 322

LARGE-SAMPLE TESTS OF HYPOTHESES 324

9.1 Testing Hypotheses about Population Parameters 325

9.2 A Statistical Test of Hypothesis 325

9.3 A Large-Sample Test about a Population Mean 328

The Essentials of the Test 329

Calculating the p-Value 332

Two Types of Errors 335

The Power of a Statistical Test 336

Exercises 339

9.4 A Large-Sample Test of Hypothesis for the Difference

between Two Population Means 341

Hypothesis Testing and Confidence Intervals 343

Exercises 344

9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion 347

Statistical Significance and Practical Importance 349

Exercises 350

9.6 A Large-Sample Test of Hypothesis for the Difference between

Two Binomial Proportions 351

Exercises 354

9.7 Some Comments on Testing Hypotheses 356

Chapter Review 357

Supplementary Exercises 358

CASE STUDY: An Aspirin a Day . . . ? 362

INFERENCE FROM SMALL SAMPLES 364

10.1 Introduction 365

10.2 Student’s t Distribution 365

Assumptions behind Student’s t Distribution 368

10.3 Small-Sample Inferences Concerning a Population Mean 369

Exercises 373

10.4 Small-Sample Inferences for the Difference between

Two Population Means: Independent Random Samples 376

Exercises 382

10.5 Small-Sample Inferences for the Difference between

Two Means: A Paired-Difference Test 386

Exercises 391

10.6 Inferences Concerning a Population Variance 394

Exercises 400

10.7 Comparing Two Population Variances 401

Exercises 407

10.8 Revisiting the Small-Sample Assumptions 409

Chapter Review 410

Technology Today 410

Supplementary Exercises 416

CASE STUDY: School Accountability Study—

How Is Your School Doing? 424

THE ANALYSIS OF VARIANCE 425

11.1 The Design of an Experiment 426

11.2 What Is an Analysis of Variance? 427

11.3 The Assumptions for an Analysis of Variance 427

11.4 The Completely Randomized Design: A One-Way Classification 428

11.5 The Analysis of Variance for a Completely Randomized Design 429

Partitioning the Total Variation in an Experiment 429

Testing the Equality of the Treatment Means 432

Estimating Differences in the Treatment Means 434

Exercises 437

11.6 Ranking Population Means 440

Exercises 443

11.7 The Randomized Block Design: A Two-Way Classification 444

11.8 The Analysis of Variance for a Randomized Block Design 445

Partitioning the Total Variation in the Experiment 445

Testing the Equality of the Treatment and Block Means 448

Identifying Differences in the Treatment and Block Means 450

Some Cautionary Comments on Blocking 451

Exercises 452

11.9 The a _ b Factorial Experiment: A Two-Way Classification 456

11.10 The Analysis of Variance for an a _ b Factorial Experiment 458

Exercises 462

11.11 Revisiting the Analysis of Variance Assumptions 466

Residual Plots 467

11.12 A Brief Summary 469

Chapter Review 469

Technology Today 470

Supplementary Exercises 475

CASE STUDY: How to Save Money on Groceries! 481

LINEAR REGRESSION AND CORRELATION 482

12.1 Introduction 483

12.2 A Simple Linear Probabilistic Model 483

12.3 The Method of Least Squares 486

12.4 An Analysis of Variance for Linear Regression 488

Exercises 491

12.5 Testing the Usefulness of the Linear Regression Model 494

Inferences Concerning b, the Slope of the Line of Means 495

The Analysis of Variance F-Test 498

Measuring the Strength of the Relationship:

The Coefficient of Determination 498

Interpreting the Results of a Significant Regression 499

Exercises 500

12.6 Diagnostic Tools for Checking the Regression Assumptions 503

Dependent Error Terms 503

Residual Plots 503

Exercises 504

12.7 Estimation and Prediction Using the Fitted Line 507

Exercises 511

12.8 Correlation Analysis 513

Exercises 517

Chapter Review 519

Technology Today 520

Supplementary Exercises 523

CASE STUDY: Is Your Car “Made in the U.S.A.”? 528

MULTIPLE REGRESSION ANALYSIS 530

13.1 Introduction 531

13.2 The Multiple Regression Model 531

13.3 A Multiple Regression Analysis 532

The Method of Least Squares 533

The Analysis of Variance for Multiple Regression 534

Testing the Usefulness of the Regression Model 535

Interpreting the Results of a Significant Regression 536

Checking the Regression Assumptions 538

Using the Regression Model for Estimation and Prediction 538

13.4 A Polynomial Regression Model 539

Exercises 542

13.5 Using Quantitative and Qualitative Predictor Variables

in a Regression Model 546

Exercises 552

13.6 Testing Sets of Regression Coefficients 555

13.7 Interpreting Residual Plots 558

13.8 Stepwise Regression Analysis 559

13.9 Misinterpreting a Regression Analysis 560

Causality 560

Multicollinearity 560

13.10 Steps to Follow When Building a Multiple Regression Model 562

Chapter Review 562

Technology Today 563

Supplementary Exercises 565

CASE STUDY: “Made in the U.S.A.”—Another Look 572

ANALYSIS OF CATEGORICAL DATA 574

14.1 A Description of the Experiment 575

14.2 Pearson’s Chi-Square Statistic 576

14.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test 577

Exercises 579

14.4 Contingency Tables: A Two-Way Classification 581

The Chi-Square Test of Independence 582

Exercises 586

14.5 Comparing Several Multinomial Populations: A Two-Way

Classification with Fixed Row or Column Totals 588

Exercises 591

14.6 The Equivalence of Statistical Tests 592

14.7 Other Applications of the Chi-Square Test 593

Chapter Review 594

Technology Today 595

Supplementary Exercises 598

CASE STUDY: Who is the Primary Breadwinner in Your Family? 604

NONPARAMETRIC STATISTICS 606

15.1 Introduction 607

15.2 The Wilcoxon Rank Sum Test: Independent Random Samples 607

Normal Approximation for the Wilcoxon Rank Sum Test 611

Exercises 614

15.3 The Sign Test for a Paired Experiment 616

Normal Approximation for the Sign Test 617

Exercises 619

15.4 A Comparison of Statistical Tests 620

15.5 The Wilcoxon Signed-Rank Test for a Paired Experiment 621

Normal Approximation for the Wilcoxon Signed-Rank Test 624

Exercises 625

15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs 627

Exercises 631

15.7 The Friedman Fr-Test for Randomized Block Designs 633

Exercises 636

15.8 Rank Correlation Coefficient 637

Exercises 641

15.9 Summary 643

Chapter Review 644

Technology Today 645

Supplementary Exercises 648

CASE STUDY: How’s Your Cholesterol Level? 653

APPENDIX I 655

Table 1 Cumulative Binomial Probabilities 656

Table 2 Cumulative Poisson Probabilities 662

Table 3 Areas under the Normal Curve 664

Table 4 Critical Values of t 667

Table 5 Critical Values of Chi-Square 668

Table 6 Percentage Points of the F Distribution 670

Table 7 Critical Values of T for the Wilcoxon Rank

Sum Test, n1 _ n2 678

Table 8 Critical Values of T for the Wilcoxon Signed-Rank

Test, n _ 5(1)50 680

Table 9 Critical Values of Spearman’s Rank Correlation Coefficient

for a One-Tailed Test 681

Table 10 Random Numbers 682

Table 11 Percentage Points of the Studentized Range, q.05(k, df ) 684

DATA SOURCES 688

ANSWERS TO SELECTED EXERCISES 700

INDEX 714

The Population and the Sample 3

Descriptive and Inferential Statistics 4

Achieving the Objective of Inferential Statistics: The Necessary Steps 4

Keys for Successful Learning 5

DESCRIBING DATA WITH GRAPHS 7

1.1 Variables and Data 8

1.2 Types of Variables 9

1.3 Graphs for Categorical Data 11

Exercises 14

1.4 Graphs for Quantitative Data 17

Pie Charts and Bar Charts 17

Line Charts 19

Dotplots 20

Stem and Leaf Plots 20

Interpreting Graphs with a Critical Eye 22

1.5 Relative Frequency Histograms 24

Exercises 28

Chapter Review 33

Technology Today 33

Supplementary Exercises 42

CASE STUDY: How Is Your Blood Pressure? 49

DESCRIBING DATA WITH NUMERICAL MEASURES 50

2.1 Describing a Set of Data with Numerical Measures 51

2.2 Measures of Center 51

Exercises 55

2.3 Measures of Variability 57

Exercises 62

2.4 On the Practical Significance of the Standard Deviation 63

2.5 A Check on the Calculation of s 67

Exercises 69

2.6 Measures of Relative Standing 72

2.7 The Five-Number Summary and the Box Plot 77

Exercises 80

Chapter Review 83

Technology Today 84

Supplementary Exercises 87

CASE STUDY: The Boys of Summer 93

DESCRIBING BIVARIATE DATA 94

3.1 Bivariate Data 95

3.2 Graphs for Categorical Variables 95

Exercises 98

3.3 Scatterplots for Two Quantitative Variables 99

3.4 Numerical Measures for Quantitative Bivariate Data 101

Exercises 107

Chapter Review 109

Technology Today 109

Supplementary Exercises 114

CASE STUDY: Are Your Dishes Really Clean? 121

PROBABILITY AND PROBABILITY DISTRIBUTIONS 123

4.1 The Role of Probability in Statistics 124

4.2 Events and the Sample Space 124

4.3 Calculating Probabilities Using Simple Events 127

Exercises 130

4.4 Useful Counting Rules (Optional) 133

Exercises 137

4.5 Event Relations and Probability Rules 139

Calculating Probabilities for Unions and Complements 141

4.6 Independence, Conditional Probability, and

the Multiplication Rule 144

Exercises 149

4.7 Bayes’ Rule (Optional) 152

Exercises 156

4.8 Discrete Random Variables and Their Probability Distributions 158

Random Variables 158

Probability Distributions 158

The Mean and Standard Deviation for a Discrete Random Variable 160

Exercises 163

Chapter Review 166

Technology Today 167

Supplementary Exercises 169

CASE STUDY: Probability and Decision Making in the Congo 174

SEVERAL USEFUL DISCRETE DISTRIBUTIONS 175

5.1 Introduction 176

5.2 The Binomial Probability Distribution 176

Exercises 185

5.3 The Poisson Probability Distribution 188

Exercises 193

5.4 The Hypergeometric Probability Distribution 194

Exercises 196

Chapter Review 197

Technology Today 198

Supplementary Exercises 202

CASE STUDY: A Mystery: Cancers Near a Reactor 208

THE NORMAL PROBABILITY DISTRIBUTION 209

6.1 Probability Distributions for Continuous Random Variables 210

6.2 The Normal Probability Distribution 213

6.3 Tabulated Areas of the Normal Probability Distribution 214

The Standard Normal Random Variable 214

Calculating Probabilities for a General Normal Random Variable 218

Exercises 221

6.4 The Normal Approximation to the Binomial Probability

Distribution (Optional) 224

Exercises 229

Chapter Review 231

Technology Today 232

Supplementary Exercises 236

CASE STUDY: “Are You Going to Curve the Grades?” 241

SAMPLING DISTRIBUTIONS 242

7.1 Introduction 243

7.2 Sampling Plans and Experimental Designs 243

Exercises 246

7.3 Statistics and Sampling Distributions 248

7.4 The Central Limit Theorem 251

7.5 The Sampling Distribution of the Sample Mean 254

Standard Error 255

Exercises 258

7.6 The Sampling Distribution of the Sample Proportion 260

Exercises 264

7.7 A Sampling Application: Statistical Process Control (Optional) 266

A Control Chart for the Process Mean: The x_ Chart 267

A Control Chart for the Proportion Defective: The p Chart 269

Exercises 271

Chapter Review 272

Technology Today 273

Supplementary Exercises 276

CASE STUDY: Sampling the Roulette at Monte Carlo 279

LARGE-SAMPLE ESTIMATION 281

8.1 Where We’ve Been 282

8.2 Where We’re Going—Statistical Inference 282

8.3 Types of Estimators 283

8.4 Point Estimation 284

Exercises 289

8.5 Interval Estimation 291

Constructing a Confidence Interval 292

Large-Sample Confidence Interval for a Population Mean m 294

Interpreting the Confidence Interval 295

Large-Sample Confidence Interval for a Population Proportion p 297

Exercises 299

8.6 Estimating the Difference between Two Population Means 301

Exercises 304

8.7 Estimating the Difference between Two Binomial Proportions 307

Exercises 309

8.8 One-Sided Confidence Bounds 311

8.9 Choosing the Sample Size 312

Exercises 316

Chapter Review 318

Supplementary Exercises 318

CASE STUDY: How Reliable Is That Poll?

CBS News: How and Where America Eats 322

LARGE-SAMPLE TESTS OF HYPOTHESES 324

9.1 Testing Hypotheses about Population Parameters 325

9.2 A Statistical Test of Hypothesis 325

9.3 A Large-Sample Test about a Population Mean 328

The Essentials of the Test 329

Calculating the p-Value 332

Two Types of Errors 335

The Power of a Statistical Test 336

Exercises 339

9.4 A Large-Sample Test of Hypothesis for the Difference

between Two Population Means 341

Hypothesis Testing and Confidence Intervals 343

Exercises 344

9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion 347

Statistical Significance and Practical Importance 349

Exercises 350

9.6 A Large-Sample Test of Hypothesis for the Difference between

Two Binomial Proportions 351

Exercises 354

9.7 Some Comments on Testing Hypotheses 356

Chapter Review 357

Supplementary Exercises 358

CASE STUDY: An Aspirin a Day . . . ? 362

INFERENCE FROM SMALL SAMPLES 364

10.1 Introduction 365

10.2 Student’s t Distribution 365

Assumptions behind Student’s t Distribution 368

10.3 Small-Sample Inferences Concerning a Population Mean 369

Exercises 373

10.4 Small-Sample Inferences for the Difference between

Two Population Means: Independent Random Samples 376

Exercises 382

10.5 Small-Sample Inferences for the Difference between

Two Means: A Paired-Difference Test 386

Exercises 391

10.6 Inferences Concerning a Population Variance 394

Exercises 400

10.7 Comparing Two Population Variances 401

Exercises 407

10.8 Revisiting the Small-Sample Assumptions 409

Chapter Review 410

Technology Today 410

Supplementary Exercises 416

CASE STUDY: School Accountability Study—

How Is Your School Doing? 424

THE ANALYSIS OF VARIANCE 425

11.1 The Design of an Experiment 426

11.2 What Is an Analysis of Variance? 427

11.3 The Assumptions for an Analysis of Variance 427

11.4 The Completely Randomized Design: A One-Way Classification 428

11.5 The Analysis of Variance for a Completely Randomized Design 429

Partitioning the Total Variation in an Experiment 429

Testing the Equality of the Treatment Means 432

Estimating Differences in the Treatment Means 434

Exercises 437

11.6 Ranking Population Means 440

Exercises 443

11.7 The Randomized Block Design: A Two-Way Classification 444

11.8 The Analysis of Variance for a Randomized Block Design 445

Partitioning the Total Variation in the Experiment 445

Testing the Equality of the Treatment and Block Means 448

Identifying Differences in the Treatment and Block Means 450

Some Cautionary Comments on Blocking 451

Exercises 452

11.9 The a _ b Factorial Experiment: A Two-Way Classification 456

11.10 The Analysis of Variance for an a _ b Factorial Experiment 458

Exercises 462

11.11 Revisiting the Analysis of Variance Assumptions 466

Residual Plots 467

11.12 A Brief Summary 469

Chapter Review 469

Technology Today 470

Supplementary Exercises 475

CASE STUDY: How to Save Money on Groceries! 481

LINEAR REGRESSION AND CORRELATION 482

12.1 Introduction 483

12.2 A Simple Linear Probabilistic Model 483

12.3 The Method of Least Squares 486

12.4 An Analysis of Variance for Linear Regression 488

Exercises 491

12.5 Testing the Usefulness of the Linear Regression Model 494

Inferences Concerning b, the Slope of the Line of Means 495

The Analysis of Variance F-Test 498

Measuring the Strength of the Relationship:

The Coefficient of Determination 498

Interpreting the Results of a Significant Regression 499

Exercises 500

12.6 Diagnostic Tools for Checking the Regression Assumptions 503

Dependent Error Terms 503

Residual Plots 503

Exercises 504

12.7 Estimation and Prediction Using the Fitted Line 507

Exercises 511

12.8 Correlation Analysis 513

Exercises 517

Chapter Review 519

Technology Today 520

Supplementary Exercises 523

CASE STUDY: Is Your Car “Made in the U.S.A.”? 528

MULTIPLE REGRESSION ANALYSIS 530

13.1 Introduction 531

13.2 The Multiple Regression Model 531

13.3 A Multiple Regression Analysis 532

The Method of Least Squares 533

The Analysis of Variance for Multiple Regression 534

Testing the Usefulness of the Regression Model 535

Interpreting the Results of a Significant Regression 536

Checking the Regression Assumptions 538

Using the Regression Model for Estimation and Prediction 538

13.4 A Polynomial Regression Model 539

Exercises 542

13.5 Using Quantitative and Qualitative Predictor Variables

in a Regression Model 546

Exercises 552

13.6 Testing Sets of Regression Coefficients 555

13.7 Interpreting Residual Plots 558

13.8 Stepwise Regression Analysis 559

13.9 Misinterpreting a Regression Analysis 560

Causality 560

Multicollinearity 560

13.10 Steps to Follow When Building a Multiple Regression Model 562

Chapter Review 562

Technology Today 563

Supplementary Exercises 565

CASE STUDY: “Made in the U.S.A.”—Another Look 572

ANALYSIS OF CATEGORICAL DATA 574

14.1 A Description of the Experiment 575

14.2 Pearson’s Chi-Square Statistic 576

14.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test 577

Exercises 579

14.4 Contingency Tables: A Two-Way Classification 581

The Chi-Square Test of Independence 582

Exercises 586

14.5 Comparing Several Multinomial Populations: A Two-Way

Classification with Fixed Row or Column Totals 588

Exercises 591

14.6 The Equivalence of Statistical Tests 592

14.7 Other Applications of the Chi-Square Test 593

Chapter Review 594

Technology Today 595

Supplementary Exercises 598

CASE STUDY: Who is the Primary Breadwinner in Your Family? 604

NONPARAMETRIC STATISTICS 606

15.1 Introduction 607

15.2 The Wilcoxon Rank Sum Test: Independent Random Samples 607

Normal Approximation for the Wilcoxon Rank Sum Test 611

Exercises 614

15.3 The Sign Test for a Paired Experiment 616

Normal Approximation for the Sign Test 617

Exercises 619

15.4 A Comparison of Statistical Tests 620

15.5 The Wilcoxon Signed-Rank Test for a Paired Experiment 621

Normal Approximation for the Wilcoxon Signed-Rank Test 624

Exercises 625

15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs 627

Exercises 631

15.7 The Friedman Fr-Test for Randomized Block Designs 633

Exercises 636

15.8 Rank Correlation Coefficient 637

Exercises 641

15.9 Summary 643

Chapter Review 644

Technology Today 645

Supplementary Exercises 648

CASE STUDY: How’s Your Cholesterol Level? 653

APPENDIX I 655

Table 1 Cumulative Binomial Probabilities 656

Table 2 Cumulative Poisson Probabilities 662

Table 3 Areas under the Normal Curve 664

Table 4 Critical Values of t 667

Table 5 Critical Values of Chi-Square 668

Table 6 Percentage Points of the F Distribution 670

Table 7 Critical Values of T for the Wilcoxon Rank

Sum Test, n1 _ n2 678

Table 8 Critical Values of T for the Wilcoxon Signed-Rank

Test, n _ 5(1)50 680

Table 9 Critical Values of Spearman’s Rank Correlation Coefficient

for a One-Tailed Test 681

Table 10 Random Numbers 682

Table 11 Percentage Points of the Studentized Range, q.05(k, df ) 684

DATA SOURCES 688

ANSWERS TO SELECTED EXERCISES 700

INDEX 714