1 Introduction 1
2 Probability:Fundamental Concepts and Operational Rules 4
2.1 Repeatable Experiments and Sample Spaces 5
2.2 Events and the Venn Diagram 6
2.3 Probability and Operational Rules 9
2.4 Conditional Probability and Statistical Independence 13
List of Figures 15
CONTENTS 15
2.5 Bayes'Formula 16
2.6 Counting Techniques:Trees,Combinations,and Permutations 17
6.1 Introduction 18
List of Tables 19
Preface 23
Exercises 23
Computer-Based Exercises 27
3 Discrete Random Variables 28
3.1 Random Variables and General Properties of Probability Distributions 29
3.2 The Binomial Distribution 34
3.3 Some Popular Discrete Distributions and Their Relationships 39
3.4 A Suggestion for Solving Problems Involving Discrete Random Variables 50
3.5 Discrete Bivariate Probability Distribution Functions 50
Exercises 55
Computer-Based Exercises 60
4 Continuous Random Variables 62
4.1 General Properties of Continuous Random Variables 63
4.2 The Normal Distribution 65
4.3 Some Popular Continuous Distributions and Their Relationships 70
4.4 Continuous Bivariate Probability Density Functions 82
Exercises 86
Computer-Based Exercises 91
5 The Mean,Variance,Expected Value Operator,and Other Functions of Random Variables 93
5.1 Introduction 94
5.2 Measures of Centrality:The Mean,Median,and Mode 94
5.3 Measures of Variability:The Range and the Variance 98
5.4 The Expected Value Operator 100
5.5 Two Additional Measures of a Probability Distribution Function:Skewness and Kurtosis 101
5.6 The Covariance and Correlation of Bivariate Distribution Functions 107
5.7 Functions of One or More Random Variables 109
5.8 A Comment about the"Road Ahead" 113
Exercises 113
6 Classification and Description of Sample Data 118
6.2 The Frequency Table and Its Outgrowths 119
6.3 Graphical Presentations of the Frequency Table 122
6.4 Sample Estimates 126
6.5 Some Suggestions for Further Study 129
Exercises 130
7 Sampling Distributions:Random Sampling,the Sample Mean and Sample Variance,and the Central Limit Theorem 137
7.1 Random Sampling from Finite and Infinite Populations 138
7.2 The Distribution of the Sample Mean,？ 142
7.3 The Distribution of the Sample Variance,S2 149
Exercises 151
8 Point and Interval Estimators and the Estimation of the Mean and the Variance 154
8.1 Point Estimators 155
8.2 Interval Estimators 157
8.3 Interval Estimates for Population Means 158
8.4 Determining an Adequate Sample Size for Interval Estimation of a Mean 163
8.5 Confidence Intervals for the Variance 163
8.6 Estimating Proportions 164
8.7 The Three General Types of Confidence Intervals 165
Exercises 167
9 Hypothesis Tests about a Single Mean,a Single Proportion,or a Single Variance 171
9.1 Introduction 172
9.2 Hypothesis Tests about a Single Mean 174
9.3 Hypothesis Tests about a Single Proportion 186
9.4 Hypothesis Tests about a Single Variance 188
9.5 Some Comments on the Difference between Statistical Significance and Practical Significance 191
Exercises 192
10 Hypothesis Tests for Two Means,Two Variances,or Two Proportions 195
10.1 Tests Comparing Two Means When σ1 and σ2 Are Known 196
10.2 Tests Comparing Two Means When σ1 and σ2 Are Unknown 199
10.3 Tests Comparing Two Means When the Data Are Paired 201
10.4 Tests Concerning Two Variances 202
10.5 Hypothesis Tests about Two Proportions 204
Exercises 207
11 Fitting Equations to Data,Part Ⅰ:Simple Linear Regression Analysis and Curvilinear Regression Analysis 211
11.1 Introduction 212
11.2 The Mathematical Model for Simple Linear Regression Analysis 213
11.3 Obtaining the Best Estimates of β0 and β1 215
11.4 The Multiple Correlation Coefficient Squared,r2 218
11.5 A Hypothesis Test for the Significance of the Fitted Line 220
11.6 The Construction of Confidence Intervals about β0,β1,the Mean of Y,and a Predicted Value of Y 222
11.7 The Correlation Coefficient and a Joint Confidence Region for β0 and β1 224
11.8 Graphical Methods of Investigating Data Structure in SLR 227
11.9 The Study of Sample Residuals in SLR 230
11.10 Curvilinear Regression 235
Exercises 240
12 Fitting Equations to Data,Part Ⅱ:Multivariate Regression Analysis 245
12.1 Introduction 246
12.2 Estimating the Parameter Values in MLR 248
12.3 Some Useful Theoretical Properties of MLR 250
12.4 The Variance-Covariance and Correlation Matrices of ？ 252
12.5 Univariate Confidence Intervals on the βi and on predicted values of y 253
12.6 Determining Whether a Fit is Adequate and Comparing Competing Models 255
Exercises 259
12.7 The General Linear Model and"the Other Side of the Coin" 259
13 Hypothesis Tests for Two or More Means:Analysis of Variance-Single-Factor Designs 265
13.1 Introduction 266
13.2 Completely Randomized Single-Factor Experiments 266
13.3 How to Determine Which Means Differ When H0 Is Rejected 271
13 4 The Operating Characteristic Curve for the Completely Randomized Single-Factor Design 275
13.5 The Randomized Block Design:A Single-Factor Design with One Restriction on Randomization 280
13.6 Some Comments on Additional Single-Factor Designs and on Missing Data 285
Exercises 286
14 Factorial Analysis of Variance 293
14.1 Introduction 293
14.2 A Two-Factor Factorial ANOVA Design 294
14.3 Higher-Order Multifactor Factorial Designs 300
Exercises 300
15 An Introduction to Statistical Quality Control 303
15.2 A Control Chart for Variables:The？-R Chart 304
15.1 Introduction 304
15.3 Control Charts for Attributes 314
15.4 Acceptance Sampling:Construction of Sampling Plans and Their Uses 319
Exercises 327
16 Some Additional Methods of Data Analysis 332
16.1 Introduction 333
16.2 The x2 Test for Goodness of Fit 333
16.3 A Distribution-Free AIternative to the t Test:The Wilcoxon Signed Rank Test 336
16.4 A Distribution-Free Alternative to the Two-Sample t Test:The Wilcoxon Rank Sum Test 341
16.5 A Distribution-Free Alternative to the Completely Randomized Single-Factor ANOVA:The Kruskal-Wallis Test 344
Exercises 346
References and Suggested Readings 349
Statistcal Tables 351
Answers to Selected Exercises 375
Index 385