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1 The Nature of Statistical Inference 1

1．Inferences and Their Accuracy 1

2．Some Definitions of Terms 2

3．The Basis for Inferences 3

4．Types of Inferences 4

5．The Precision of Inferences 4

2 The Objective of a Sampling Experiment 6

1．The Importance of Operational Definitions 7

2．Defining the Observational Unit 8

3．Defining the One or More Populations 9

4．Defining the Population Parameter 11

5．Defining the Type of Inference 14

6．Defining the Precision in Inferences 14

3 The Variability Among Observations 16

1．Procedure for Estimating Variability 17

2．Designs for Reducing Variability 17

3．Stratified Random Sampling 18

4．Blocking Designs 19

5．Estimating the Components of Sampling Error 20

6．Estimating Variability Using a Double Sampling Procedure 22

4 The Power-Function Approach 24

1．Estimation Problems 25

2．Tests of Hypotheses 27

3．Selection Problems 29

4．Stating the Precision Desired in an Inference 32

5 Estimation Problems 34

1．Confidence Interval for Normal Means 35

2．Confidence Interval for Difference Between Two Nor-mal Means with Two Independent Samples from Populations with a Common Variance 37

3．Confidence Interval for Difference Between Two Nor-mal Means with Two Independent Samples from Populations with Unequal Variances 40

4．Confidence Interval for the Mean Difference Between Paired Observations from a Bivariate Normal Distri-bution 43

5．Confidence Interval for Any One of Several Normal Means with Independent Samples from Populations with a Common Variance 46

6．Confidence Interval for Difference Between Any Pair of Several Normal Means with Independent Samples from Populations with a Common Variance 49

7．Confidence Interval for Any Contrast Among Several Normal Means with Independent Samples from Pop-ulations with a Common Variance 52

8．Confidence Interval for Normal Variances 56

9．Confidence Interval for the Ratio of Two Normal Variances 58

10．Confidence Intervals for Binomial Proportions 61

11．Confidence Interval for Exponential Scale Parameters 63

12．Confidence Interval for the Ratio of Two Exponential Scale Parameters 65

13．Upper Bound on Confidence Interval for Means When Variance is Known 68

14．Tolerance Limits for the Percentile Range of a Variable 69

15．Confidence Band for Cumulative Distribution Func-tions 70

6 Test of Hypotheses 73

1．Tests of Hypotheses About Normal Means 74

2．Tests of Hypotheses About Difference Between Two Normal Means with Two Independent Samples from Populations with a Common Variance 77

3．Tests of Hypotheses About Difference Between Two Normal Means With Two Independent Samples from Populations with Unequal Variances 81

4．Tests of Hypotheses About the Mean Difference Be-tween Paired Observations from a Bivariate Normal Distribution 84

5．Tests of Hypotheses About the Equality of Several Normal Means with Independent Samples from Pop-ulations with a Common Variance 88

6．Tests of Hypotheses About Normal Variances 91

7．Tests of Hypotheses About the Ratio of Two Normal Variances 94

8．Tests of Hypotheses About Binomial Proportions 98

9．Tests of Hypotheses About the Equality of Two Bi-nomial Proportions 101

10．Tests of Hypotheses About the Equality of Several Binomial Proportions 104

11．Tests of Hypotheses About Exponential Scale Pa-rameters 107

12．Tests of Hypotheses About the Ratio of Two Expo-nential Scale Parameters 110

7 Selection Problems 114

1．Selecting the Best of Several Normal Means with Independent Samples from Populations with a Com-mon Variance 115

2．Selecting the Best of Several Normal Variances 119

3．Selecting the Best of Several Binomial Proportions 122

4．Selecting the Best of Several Exponential Scale Pa-rameters 126

8 Sequential Sampling 129

1．Sequential Tests of Hypotheses About Normal Means 132

2．Sequential Tests of Hypotheses About Normal Vari-ances 136

3．Sequential Tests of Hypotheses About Binomial Pro-portions 140

4．Sequential Tests of Hypotheses About Exponential Scale Parameters 143

9 Lot Acceptance Sampling Plans 147

1．Military Standard 105 C 150

2．Military Standard 414 156

10 Sample-Size Precision Schedules 163

1．Case Example:An Estimation Problem 166

2．Case Example:A Test of Hypothesis 167

3．Case Example:A Selection Problem 171

11 Decision-Function Approach 174

1．Estimating a Mean with Losses Proportional to the Square of the Error in the Estimate 177

2．Estimating a Normal Mean with Losses Proportional to the Absolute Value of the Error in the Estimate 178

3．Selecting the Best of Several Normal Means with In-dependent Samples from Populations with a Com-mon Variance 180

4．Selecting the Better of Two Binomial Proportions 182

5．Testing a Hypothesis About a Normal Mean with Loss from Acceptance and Loss from Rejection Linear Functions of the True but Unknown Population Mean 185

6．Testing a Hypothesis About a Binomial Proportion with Loss from Acceptance and Loss from Rejection Linear Functions of the True but Unknown Binomial Proportion 187

References 190

Appendix Tables 193

TABLE 1．Upper Percentage Points of the t Distribution 195

TABLE 2．Upper Percentage Points of the x2 Distribu-tion 196

TABLE 3．Upper 10 Percentage Points of the F Distri-bution 198

TABLE 4．Upper 5 Percentage Points of the F Distri-bution 200

TABLE 5．Upper 1 Percentage Points of the F Distri-bution 202

TABLE 6．Upper Percentage Points of the Noncentral t Distribution when the Probability of Erroneously Reject-ing the Test Hypothesis(α)Equals 0．05 204

TABLE 7．Upper Percentage Points of the Noncentral t Distribution when the Probability of Erroneously Reject-ing the Test Hypothesis(α)Equals 0．01 205

TABLE 8．Upper Percentage Points of the Noncentral x2 Distribution when the Probability of Erroneously Re-jecting the Test Hypothesis(α)Equals 0．05 206

TABLE 9．Upper Percentage Points of the Noncentral x2 Distribution when the Probability of Erroneously Re-jecting the Test Hypothesis(α)Equals 0．01 207

TABLE 10．Upper 20 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．05 208

TABLE 11．Upper 20 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．01 209

TABLE 12．Upper 30 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．05 210

TABLE 13．Upper 30 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．01 211

TABLE 14．Upper 5 Percentage Points of the Multi-variate t Distribution with Correlations Plus One Half 212

TABLE 15．Upper 1 Percentage Points of the Multi-variate t Distribution with Correlations Plus One Half 213

TABLE 16．Upper 10 Percentage Points of the Student-ized Range,(xn－x1)/s 214

TABLE 17．Upper 5 Percentage Points of the Student-ized Range,(xn－x1)/s 216

TABLE 18．Upper 1 Percentage Points of the Student-ized Range,(xn－x1)/s 218

TABLE 19．Upper Percentage Points of d(n,the Maxi-mum Absolute Difference Between Sample and Popula-tion Cumulative Distributions 220

TABLE 20．y=2 arcsin ？ 221

Index 223