Chapter Ⅰ Introduction to Statistics 1
1.1 Introduction 1
1.2 Data Collection and Descriptive Statistics 1
1.3 Inferential Statistics and Probability Models 2
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 17
2.3.2 Sample Variance and Sample Standard Deviation 22
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 Coefficient 33
Problems 41
Chapter 3 Elements of Probability 55
3.1 Introduction 55
3.2 Sample Space and Events 56
3.3 Venn Diagrams and the Algebra of Events 58
3.4 Axioms of Probability 59
3.5 Sample Spaces Having Equally Likely Outcomes 61
3.6 Conditional Probability 67
3.7 Bayes’Formula 70
3.8 Independent Events 76
Problems 80
Chapter 4 Random Variables and Expectation 89
4.1 Random Variables 89
4.2 Types of Random Variables 92
4.3 Jointly 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 125
4.9 Chebyshev’s Inequality and the Weak Law of Large Numbers 127
Problems 130
Chapter 5 Special Random Variables 141
5.1 The 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 Poisson Distribution Function 155
5.3 The Hypergeometric Random Variable 156
5.4 The Uniform Random Variable 160
5.5 Normal Random Variables 168
5.6 Exponential Random Variables 176
5.6.1 The Poisson Process 180
5.7 The Gamma Distribution 183
5.8 Distributions Arising from the Normal 186
5.8.1 The Chi-Square Distribution 186
5.8.2 The t-Distribution 190
5.8.3 The F-Distribution 192
5.9 The Logistics Distribution 193
Problems 195
Chapter 6 Distributions of Sampling Statistics 203
6.1 Introduction 203
6.2 The Sample Mean 204
6.3 The Central Limit Theorem 206
6.3.1 Approximate Distribution of the Sample Mean 212
6.3.2 How Large a Sample Is Needed？ 214
6.4 The Sample Variance 215
6.5 Sampling Distributions from a Normal Population 216
6.5.1 Distribution of the Sample Mean 217
6.5.2 Joint Distribution of X and S2 217
6.6 Sampling from a Finite Population 219
Problems 223
Chapter 7 Parameter Estimation 231
7.1 Introduction 231
7.2 Maximum Likelihood Estimators 232
7.2.1 Estimating Life Distributions 240
7.3 Interval Estimates 242
7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown 248
7.3.2 Confidence Intervals for the Variance of a Normal Distribution 253
7.4 Estimating the Difference in Means of Two Normal Populations 255
7.5 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable 262
7.6 Confidence Interval of the Mean of the Exponential Distribution 267
7.7 Evaluating a Point Estimator 268
7.8 The Bayes Estimator 274
Problems 279
Chapter 8 Hypothesis Testing 293
8.1 Introduction 294
8.2 Significance Levels 294
8.3 Tests Concerning the Mean of a Normal Population 295
8.3.1 Case of Known Variance 295
8.3.2 Case of Unknown Variance：The t-Test 307
8.4 Testing the Equality of Means of Two Normal Populations 314
8.4.1 Case of Known Variances 314
8.4.2 Case of Unknown Variances 316
8.4.3 Case of Unknown and Unequal Variances 320
8.4.4 The Paired t-Test 321
8.5 Hypothesis Tests Concerning the Variance of a Normal Population 323
8.5.1 Testing for the Equality of Variances of Two Normal Populations 324
8.6 Hypothesis Tests in Bernoulli Populations 325
8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations 329
8.7 Tests Concerning the Mean of a Poisson Distribution 332
8.7.1 Testing the Relationship Between Two Poisson Parameters 333
Problems 336
Chapter 9 Regression 353
9.1 Introduction 353
9.2 Least Squares Estimators of the Regression Parameters 355
9.3 Distribution of the Estimators 357
9.4 Statistical Inferences About the Regression Parameters 363
9.4.1 Inferences Concerning β 364
9.4.2 Inferences Concerning α 372
9.4.3 Inferences Concerning the Mean Response α＋βx0 373
9.4.4 Prediction Interval of a Future Response 375
9.4.5 Summary of Distributional Results 377
9.5 The Coefficient of Determination and the Sample Correlation Coefficient 378
9.6 Analysis of Residuals：Assessing the Model 380
9.7 Transforming to Linearity 383
9.8 Weighted Least Squares 386
9.9 Polynomial Regression 393
9.10 Multiple Linear Regression 396
9.10.1 Predicting Future Responses 407
9.11 Logistic Regression Models for Binary Output Data 412
Problems 415
Chapter 10 Analysis of Variance 441
10.1 Introduction 441
10.2 An Overview 442
10.3 One-Way Analysis of Variance 444
10.3.1 Multiple Comparisons of Sample Means 452
10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes 454
10.4 Two-Factor Analysis of Variance：Introduction and Parameter Estimation 456
10.5 Two-Factor Analysis of Variance：Testing Hypotheses 460
10.6 Two-Way Analysis of Variance with Interaction 465
Problems 473
Chapter Ⅱ Goodness of Fit Tests and Categorical Data Analysis 485
11.1 Introduction 485
11.2 Goodness of Fit Tests When All Parameters Are Specified 486
11.2.1 Determining the Critical Region by Simulation 492
11.3 Goodness of Fit Tests When Some Parameters Are Unspecified 495
11.4 Tests of Independence in Contingency Tables 497
11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals 501
11.6 The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Data 506
Problems 510
Chapter 12 Nonparametric Hypothesis Tests 517
12.1 Introduction 517
12.2 The Sign Test 517
12.3 The Signed Rank Test 521
12.4 The Two-Sample Problem 527
12.4.1 The Classical Approximation and Simulation 531
12.5 The Runs Test for Randomness 535
Problems 539
Chapter 13 Quality Control 547
13.1 Introduction 547
13.2 Control Charts for Average Values：The X-Control Chart 548
13.2.1 Case of Unknown μ and σ 551
13.3 S-Control Charts 556
13.4 Control Charts for the Fraction Defective 559
13.5 Control Charts for Number of Defects 561
13.6 Other Control Charts for Detecting Changes in the Population Mean 565
13.6.1 Moving-Average Control Charts 565
13.6.2 Exponentially Weighted Moving-Average Control Charts 567
13.6.3 Cumulative Sum Control Charts 573
Problems 575
Chapter 14 Life Testing 583
14.1 Introduction 583
14.2 Hazard Rate Functions 583
14.3 The Exponential Distribution in Life Testing 586
14.3.1 Simultaneous Testing——Stopping at the rth Failure 586
14.3.2 Sequential Testing 592
14.3.3 Simultaneous Testing—— Stopping by a Fixed Time 596
14.3.4 The Bayesian Approach 598
14.4 A Two-Sample Problem 600
14.5 The Weibull Distribution in Life Testing 602
14.5.1 Parameter Estimation by Least Squares 604
Problems 606
Chapter 15 Simulation，Bootstrap Statistical Methods，and Permutation Tests 613
15.1 Introduction 613
15.2 Random Numbers 614
15.2.1 The Monte Carlo Simulation Approach 616
15.3 The Bootstrap Method 617
15.4 Permutation Tests 624
15.4.1 Normal Approximations in Permutation Tests 627
15.4.2 Two-Sample Permutation Tests 631
15.5 Generating Discrete Random Variables 632
15.6 Generating Continuous Random Variables 634
15.6.1 Generating a Normal Random Variable 636
15.7 Determining the Number of Simulation Runs in a Monte Carlo Study 637
Problems 638
Appendix of Tables 641
Index 647