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1 Introduction1

1.1 Statistical Inference1

1.2 Statistical Investigation3

1.3 Population and Sample4

1.4 Frequency Distribution7

1.5 Frequency Distribution—An Analysis Tool10

1.6 Other Frequency Distribution Representation12

1.7 Summation Operations15

1.8 Descriptive Measures17

1.9 Measures of Location18

1.10 Arithmetic Mean18

1.11 Mean of Means20

1.12 Other Measures of Average21

1.13 Measures of Variation28

1.14 Computation of Variance32

1.15 Change of Scale （Data Coding）34

1.16 Z-transformation38

1.17 Moments39

1.18 Significant Digits and Data Accuracy41

2 Elementary Probability50

2.1 Fundamental Principle for Counting50

2.2 Factorials52

2.3 Combinations53

2.4 Probability55

2.5 Operations with Events and Probabilities57

2.6 Conditional Probability60

2.7 Baye’s Theorem of Inverse Probability61

2.8 Relative Frequency Probability62

2.9 Probability Based on Algebra of Sets63

3 Probability Distributions68

3.1 Random Variable68

3.2 Probability Function71

3.3 Cumulative Distribution Function71

3.4 Continuous Random Variables73

3.5 Probability Distribution Table76

4 Discrete Distribution Model84

4.1 Mathematical Expectation84

4.2 Chebyshev’s Inequality88

4.3 Characteristic Function of a Distribution89

4.4 Bernoulli Distribution Model92

4.5 Binomial Distribution Model94

4.6 Poisson Distribution Model101

4.7 Hypergeometric Distribution Model106

4.8 Summary—Discrete Models108

4.9 Other Discrete Models110

5 Normal Distribution Model120

5.1 The Normal Distribution120

5.2 Properties of the Normal Distribution121

5.3 Normal Model in Standard Form122

5.4 Normal Approximation to the Binomial129

5.5 Normalizing Transformation132

5.6 Central Limit Theorem133

5.7 Sampling Distribution of the Mean134

5.8 Specifications136

5.9 Combinations of Independent Random Variables139

6 Continuous Distributions Model156

6.1 Degrees of Freedom156

6.2 Chi-Square Distribution Model158

6.3 Student’s t-Distribution Model163

6.4 F-Distribution Model165

6.5 Distribution of x168

6.6 Distributions Related to s 2 x170

6.7 Distribution of x-y171

7 Hypothesis Testing and Estimation178

7.1 Rationale of Hypothesis Testing179

7.2 Nomenclature181

7.3 Hypothesis Test Concerning the Mean，with Standard Deviation Known182

7.4 Type Ⅱ Error and β185

7.5 One and Two-Sided Tests191

7.6 α，β，n Relationships195

7.7 Analytic Solution for β or n198

7.8 Summary—Test of the Mean with Standard Deviation Known201

7.9 Test of the Mean with Standard Deviation Unknown202

7.10 Test That Two Means Are Equal207

7.11 Test That Two Means Are Equal，Paired Observations213

7.12 Test of the Standard Deviation of a Normal Population218

7.13 Test That Two Standard Deviations Are Equal （Normal Populations）226

7.14 Test of the Proportion232

7.15 Test of Goodness of Fit239

7.16 The Estimation Problem247

7.17 Rationale of Estimation249

8 Quality Control266

8.1 Process Capability266

8.2 Process Control270

8.3 Sampling Inspection279

8.4 Operating Characteristic Curve280

8.5 Sampling Plan Evaluation283

8.6 Sampling Plan Design285

8.7 Variables Sampling Plans287

9 Curve Fitting298

9.1 Method of Moments299

9.2 Method of Least Squares302

9.3 Fitting a Polynomial305

9.4 Fitting an Exponential308

9.5 Choice of Model310

9.6 Fitting a Distribution Function311

10 Regression and Correlation318

10.1 The Regression Problem318

10.2 Significance of Regression321

10.3 Hypothesis Tests—Slope and Intercept325

10.4 Confidence Interval Estimates—Slope and Intercept328

10.5 Confidence Interval Estimate of μY？X329

10.6 Confidence Interval Estimate of Y0330

10.7 Correlation333

10.8 Inferences Regarding β336

10.9 Multiple Linear Regression339

10.10 Significance of Addition of a Variable to the Regression Equation342

10.11 Additional Remarks—Regression and Correlation344

11 Analysis of Variance352

11.1 Single Variable，Completely Randomized Design353

11.2 Randomized Complete Block Design362

11.3 Latin Square Design367

11.4 Introduction to Factorial Design369

12 Processing of Statistical Data382

12.1 Desk Calculator Computation382

12.2 Digital Computer Calculation389

Appendices395

A Cumulative Binomial Distribution397

B Cumulative Poisson Distribution403

C The Hypergeometric Distribution408

D Tail Areas—The Normal Distribution411

E The Chi-Square Distribution413

F The t-Distribution416

G The F-Distribution418

H Quality Control Chart Coefficients429

I Random Numbers431

I ndex439