1 Introduction 1
1.1 Statistical Inference 1
1.2 Statistical Investigation 3
1.3 Population and Sample 4
1.4 Frequency Distribution 7
1.5 Frequency Distribution—An Analysis Tool 10
1.6 Other Frequency Distribution Representation 12
1.7 Summation Operations 15
1.8 Descriptive Measures 17
1.9 Measures of Location 18
1.10 Arithmetic Mean 18
1.11 Mean of Means 20
1.12 Other Measures of Average 21
1.13 Measures of Variation 28
1.14 Computation of Variance 32
1.15 Change of Scale （Data Coding） 34
1.16 Z-transformation 38
1.17 Moments 39
1.18 Significant Digits and Data Accuracy 41
2 Elementary Probability 50
2.1 Fundamental Principle for Counting 50
2.2 Factorials 52
2.3 Combinations 53
2.4 Probability 55
2.5 Operations with Events and Probabilities 57
2.6 Conditional Probability 60
2.7 Baye’s Theorem of Inverse Probability 61
2.8 Relative Frequency Probability 62
2.9 Probability Based on Algebra of Sets 63
3 Probability Distributions 68
3.1 Random Variable 68
3.2 Probability Function 71
3.3 Cumulative Distribution Function 71
3.4 Continuous Random Variables 73
3.5 Probability Distribution Table 76
4 Discrete Distribution Model 84
4.1 Mathematical Expectation 84
4.2 Chebyshev’s Inequality 88
4.3 Characteristic Function of a Distribution 89
4.4 Bernoulli Distribution Model 92
4.5 Binomial Distribution Model 94
4.6 Poisson Distribution Model 101
4.7 Hypergeometric Distribution Model 106
4.8 Summary—Discrete Models 108
4.9 Other Discrete Models 110
5 Normal Distribution Model 120
5.1 The Normal Distribution 120
5.2 Properties of the Normal Distribution 121
5.3 Normal Model in Standard Form 122
5.4 Normal Approximation to the Binomial 129
5.5 Normalizing Transformation 132
5.6 Central Limit Theorem 133
5.7 Sampling Distribution of the Mean 134
5.8 Specifications 136
5.9 Combinations of Independent Random Variables 139
6 Continuous Distributions Model 156
6.1 Degrees of Freedom 156
6.2 Chi-Square Distribution Model 158
6.3 Student’s t-Distribution Model 163
6.4 F-Distribution Model 165
6.5 Distribution of x 168
6.6 Distributions Related to s 2 x 170
6.7 Distribution of x-y 171
7 Hypothesis Testing and Estimation 178
7.1 Rationale of Hypothesis Testing 179
7.2 Nomenclature 181
7.3 Hypothesis Test Concerning the Mean，with Standard Deviation Known 182
7.4 Type Ⅱ Error and β 185
7.5 One and Two-Sided Tests 191
7.6 α，β，n Relationships 195
7.7 Analytic Solution for β or n 198
7.8 Summary—Test of the Mean with Standard Deviation Known 201
7.9 Test of the Mean with Standard Deviation Unknown 202
7.10 Test That Two Means Are Equal 207
7.11 Test That Two Means Are Equal，Paired Observations 213
7.12 Test of the Standard Deviation of a Normal Population 218
7.13 Test That Two Standard Deviations Are Equal （Normal Populations） 226
7.14 Test of the Proportion 232
7.15 Test of Goodness of Fit 239
7.16 The Estimation Problem 247
7.17 Rationale of Estimation 249
8 Quality Control 266
8.1 Process Capability 266
8.2 Process Control 270
8.3 Sampling Inspection 279
8.4 Operating Characteristic Curve 280
8.5 Sampling Plan Evaluation 283
8.6 Sampling Plan Design 285
8.7 Variables Sampling Plans 287
9 Curve Fitting 298
9.1 Method of Moments 299
9.2 Method of Least Squares 302
9.3 Fitting a Polynomial 305
9.4 Fitting an Exponential 308
9.5 Choice of Model 310
9.6 Fitting a Distribution Function 311
10 Regression and Correlation 318
10.1 The Regression Problem 318
10.2 Significance of Regression 321
10.3 Hypothesis Tests—Slope and Intercept 325
10.4 Confidence Interval Estimates—Slope and Intercept 328
10.5 Confidence Interval Estimate of μY？X 329
10.6 Confidence Interval Estimate of Y0 330
10.7 Correlation 333
10.8 Inferences Regarding β 336
10.9 Multiple Linear Regression 339
10.10 Significance of Addition of a Variable to the Regression Equation 342
10.11 Additional Remarks—Regression and Correlation 344
11 Analysis of Variance 352
11.1 Single Variable，Completely Randomized Design 353
11.2 Randomized Complete Block Design 362
11.3 Latin Square Design 367
11.4 Introduction to Factorial Design 369
12 Processing of Statistical Data 382
12.1 Desk Calculator Computation 382
12.2 Digital Computer Calculation 389
Appendices 395
A Cumulative Binomial Distribution 397
B Cumulative Poisson Distribution 403
C The Hypergeometric Distribution 408
D Tail Areas—The Normal Distribution 411
E The Chi-Square Distribution 413
F The t-Distribution 416
G The F-Distribution 418
H Quality Control Chart Coefficients 429
I Random Numbers 431
I ndex 439