The fifth cdition of this book continues to demonstrate how to apply probability theory to gain insight into real,everyday statistical problems and situationsAs in the previous editions, carefully developed coverage of probability motivates probabilistic models of real phenomena and the statistical procedures that follow This approach ultimately results in an intuitive understanding of statistical procedures and strategies most often used by practicing engineers and scientistsThis book has been written for an introductory course in statistics or in probability and statistics for students in engineering, computer science,mathematics, statistics,and the natural sciences As such it assumes knowledge of elementary calculus

Preface xili

Chapter 1 Introduction to Statistics 1

1.1ntroduction 1

1.2Data Collection and Descriptive Statistics 1

1.3 Inferential Statistics and Probability Models 1

1.4 Populations and Samples 3

1.5 A Brief History of Statistics 3

Problems 7

Chapter 2 Descriptive Statistics 9

2.1 Introduction 9

2.2 Describing Data Sets 9

      2.2.1 Frequency Tables and Graphs 10

      2.2.2 Relative Frequency Tables and Graphs 10

      2.2.3 Grouped Data, Histograms,Ogives,and Stem and Leaf Plots 14

2.3 Summarizing Data Sets 17

      2.3.1 Sample Mean,Sample Median,and Sample Mode 22

      2.3.2 Sample Variance and Sample Standard Deviation 24

      2.3.3 Sample Percentiles and Box Plots 24

2.4 Chebyshev's Inequality 27

2.5 Normal Data Sets 31

2.6 Paired Data Sets and the Sample Correlation Coefficient34

Problems 41

Chapter 3 Elements of Probability53

3.1 Introduction 53

3.2 Sample Space and Events 54

3.3 Venn Diagrams and the Algebra of Events 56

3.4 Axioms of Probability 57

3.5 Sample Spaces Having Equally Likely Outcomes 59

3.6Conditional Probability 65

3.7 Bayes Formula 68

3.8 Independent Events 75

Problems 79

Chapter 4 Random Variables and Expectation 89

4.1 Random Variables 89

4.2 Types of Random Variables 92

4.3 Jointy Distributed Random Variables 95

      4.3.1 Independent Random Variables 101

      *4.3.2 Conditional Distributions 105

4.4 Expectation 107

4.5 Properties of the Expected Value 111

      4.5.1 Expected Value Of Sums Of Random Variables 115

      4.6 Variance 118

      4.7 Covariance and Variance of Sums of Random Variables 121

      4.8 Moment Generating Functions 127

      4.9 Chebyshev's Inequality and the WeakLaw ofLarge Numbers 128

      Problems 131

Chapter 5 Special Random Variables 141

5.1The Bernoulli and Binomial Random Variables 141

      5.1.1 Computing the Binomial Distribution Function 147

5.2 The Poisson Random Variable 148

      5.2.1 Computing the Poison Distribution Function 155

5.3 The Hypergeometric Random Variable 156

5.4 The Uniform Random Variable 160

5.5Normal Random Variables 168

5.6 Exponential Random Variables 177

      *5.6.1 The Poisson Process 181

      *5.6.2 The Pareto Distribution 183

5.7 The Gamma Distribution186

5.8 Distributions Arising from the Normal 188

      5.8.1 The Chi-Square Distribution 188

      5.8.2 The t-Distribution 193

      5.8.3 The F-Distribution 195

      5.9 The Logistics Distribution 196

      Problems 197

Chapter 6 Distributions of Sampling Statistics 207

6.1 Introduction 207

6.2 The Sample Mean 208

6.3 The Central Limit Theorem 210

      6.3.1 Approximate Distribution of the Sample Mean 216

      6.3.2 How Large a Sample Is Needed? 218

6.4 The Sample Variance 219

6.5 Sampling Distributions from a Normal Population 220

      6.5.1 Distribution of the Sample Mean 221

      6.5.2 Joint Distribution ofX and s2 221

6.6 Sampling from a Finite Population 223

Problems 227

Chapter7 Parameter Estimation 235

7.1 Introduction 235

7.2 Maximum Likelihood Estimators 236

      *7.2.1 Estimating Life Distributions 245

7.3 Interval Estimates247

      7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown 252

      7.3.2 Prediction Intervals 257

      7.3.3 Confidence Intervals for the Variance of a Normal Distribution 259

7.4 Estimating the Difference in Means of Two Normal Populations 260

7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable 268

*7.6 Confidence Interval of the Mean of the Exponential Distribution 272

*7.7 Evaluating a Point Estimator 273

*7.8 The Bayes Estimator.279

Problems 285

Chapter 8 Hypothesis Testing 297

8.1 Introduction 297

8.2 Significance Levels 298

8.3 Tests Concerning the Mean of a Normal Population299

      8.3.1 Case of Known Variance 299

      8.3.2 Case of Unknown Variance: The t-Test 311

8.4 Testing the Equality of Means of Two Normal Populations 318

      8.4.1 Case of Known Variances 318

      8.4.2 Case of Unknown Variances 320

      8.4.3 Case of Unknown and Unequal Variances 324

      8.4.4 The Paired t-Test 325

8.5 Hypothesis Tests Concerning the Variance of a Normal Population 327

      8.5.1 Testing for the Equality of Variances of Two Normal Populations 328

8.6 Hypothesis Tests in Bernoulli Populations

      8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations 333

8.7 Tests Concerning the Mean ofa Poisson Distribution 336

      8.7.1 Testing the Relationship Between Two Poisson Parameters 337

      Problems 339

Chapter 9 Regression 357

9.1 Introduction 357

9.2 Least Squares Estimators of the Regression Parameters 359

9.3 Distribution of the Estimators 361

9.4 Statistical Inferences About the Regression Parameters 367

      9.4.1 Inferences Concerning β 368

      9.4.2 Inferences Concerning α 376

      9.4.3 Inferences Concerning the Mean Responseα＋β 377

      9.4.4 Prediction Interval ofa Future Response379

      9.4.5 Summary of Distributional Results 381

9.5The Coefficient of Determination and the Sample Correlation Coefficient 382

9.6 Analysis of Residuals: Assessing the Model 384

9.7 Transforming to Linearity 387

9.8 Weighted Least Squares 390

9.9 Polynomial Regression 397

*9.10 Multiple Linear Regression 400

9.10.I Predicting Future Responses 411

9.10.2 Dummy Variables for Categorical Data 416

9.11 Logistic Regression Models for Binary Output Data 418

Problems 421

Chapter 10 Analysis of Variance 445

10.1 Introduction 445

10.2 An Overview 446

10.3 One-Way Analysis of Variance 448

      10.3.1 Muliple Comparisons of Sample Means 456

      10.3.2 One-Way Analysis ofVariance with Unequal Sample Sizes 458

10.4Two-Factor Analysis of Variance: Introduction and Parameter Estimation 604

10.5 Two-Factor Analysis of Variance: Testing Hypotheses 464 10.6 Two-Way Analysis of Variance with Interaction 469 Problems 477

Chapter 11 Goodness of Fit Tests and Categorical Data Analysis 489

11.1 Introduction 489

11.2 Goodness of Fit Tests When All Parameters are Specified 490

      11.2.1 Determining the Critical Region by Simulation 496

11.3 Goodness of Fit Tests When Some Parameters are Unspecified 499

11.4 Tests of Independence in Contingency Tables 501

11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals505

*11.6 The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Data 510

Problems 514

Chapter I2 Nonparametric Hypothesis Tests 521

12.1 Introduction 521

12.2 The Sign Test 521

12.3 The Signed Rank Test 525

12.4 The Two-Samp1e Problem 531

      *12.4.1 The Classical Approximation and Simulation

      12.4.2 Testing the Equality of Multiple Probability Distributions 539

12.5 The Runs Test for Randomness541

Problems 545

Chapter 13 Quality Control 553

13.1 Introduction 553

13.2 Control Charts for Average Values: The X-Control Chart 554

      *13.2.1 Case of Unknown μ and σ 557

13.3 S-Control Charts 562

13.4 Control Charts for the Fraction Defective 565

13.5 Control Charts for Number of Defects 567

13.6 Other Control Charts for Detecting Changes in the Population Mean 571

      13.6.1 Moving-Average Control Charts 571

      13.6.2 Exponentially Weighted Moving-Average Control Charts 573

      13.6.3 Cumulative Sum Control Charts579

Problems 581

Chapter 14*Life Testing 589

14.1 Introduction 589

14.2 Hazard Rate Functions 589

14.3 The Exponential Distribution in Life Testing 592

      14.3.1 Simultaneous Testing—Stopping at the rth Failure 92

      14.3.2 Sequential Testing 598

      14.3.3 Simultaneous Testing—Stopping by a Fixed Time 602

      14.3.4 The Bayesian Approach 604

14.4 A Two-Sample Problem 606

14.5 The Weibull Distribution in Life Testing608

      14.5.1 Parameter Estimation by Least Squares 610

Problems 612

Chapter 15 Simulation, Bootstrap Statistical Methods,and Permutation Tests 619

15.1 Introduction 619

15.2 Random Numbers 620

      15.2.1 The Monte Carlo Simulation Approach 622

15.3 The Bootstrap Method 623

15.4 Permutation Tests 630

      15.4.1 Normal Approximations in Permutation Tests 633 15.4.2 Two-Sample Permutation Tests 637

15.5 Generating Discrete Random Variables 638

15.6 Generating Continuous Random Variables 640

      15.6.1 Generating a Normal Random Variable 642

15.7 Determining the Number of Simulation Runs in a Monte Carlo Study 643

Problems 644

Appendix of Tables 647

IndeX 653

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