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1 The Nature of Statistical Inference1

1．Inferences and Their Accuracy1

2．Some Definitions of Terms2

3．The Basis for Inferences3

4．Types of Inferences4

5．The Precision of Inferences4

2 The Objective of a Sampling Experiment6

1．The Importance of Operational Definitions7

2．Defining the Observational Unit8

3．Defining the One or More Populations9

4．Defining the Population Parameter11

5．Defining the Type of Inference14

6．Defining the Precision in Inferences14

3 The Variability Among Observations16

1．Procedure for Estimating Variability17

2．Designs for Reducing Variability17

3．Stratified Random Sampling18

4．Blocking Designs19

5．Estimating the Components of Sampling Error20

6．Estimating Variability Using a Double Sampling Procedure22

4 The Power-Function Approach24

1．Estimation Problems25

2．Tests of Hypotheses27

3．Selection Problems29

4．Stating the Precision Desired in an Inference32

5 Estimation Problems34

1．Confidence Interval for Normal Means35

2．Confidence Interval for Difference Between Two Nor-mal Means with Two Independent Samples from Populations with a Common Variance37

3．Confidence Interval for Difference Between Two Nor-mal Means with Two Independent Samples from Populations with Unequal Variances40

4．Confidence Interval for the Mean Difference Between Paired Observations from a Bivariate Normal Distri-bution43

5．Confidence Interval for Any One of Several Normal Means with Independent Samples from Populations with a Common Variance46

6．Confidence Interval for Difference Between Any Pair of Several Normal Means with Independent Samples from Populations with a Common Variance49

7．Confidence Interval for Any Contrast Among Several Normal Means with Independent Samples from Pop-ulations with a Common Variance52

8．Confidence Interval for Normal Variances56

9．Confidence Interval for the Ratio of Two Normal Variances58

10．Confidence Intervals for Binomial Proportions61

11．Confidence Interval for Exponential Scale Parameters63

12．Confidence Interval for the Ratio of Two Exponential Scale Parameters65

13．Upper Bound on Confidence Interval for Means When Variance is Known68

14．Tolerance Limits for the Percentile Range of a Variable69

15．Confidence Band for Cumulative Distribution Func-tions70

6 Test of Hypotheses73

1．Tests of Hypotheses About Normal Means74

2．Tests of Hypotheses About Difference Between Two Normal Means with Two Independent Samples from Populations with a Common Variance77

3．Tests of Hypotheses About Difference Between Two Normal Means With Two Independent Samples from Populations with Unequal Variances81

4．Tests of Hypotheses About the Mean Difference Be-tween Paired Observations from a Bivariate Normal Distribution84

5．Tests of Hypotheses About the Equality of Several Normal Means with Independent Samples from Pop-ulations with a Common Variance88

6．Tests of Hypotheses About Normal Variances91

7．Tests of Hypotheses About the Ratio of Two Normal Variances94

8．Tests of Hypotheses About Binomial Proportions98

9．Tests of Hypotheses About the Equality of Two Bi-nomial Proportions101

10．Tests of Hypotheses About the Equality of Several Binomial Proportions104

11．Tests of Hypotheses About Exponential Scale Pa-rameters107

12．Tests of Hypotheses About the Ratio of Two Expo-nential Scale Parameters110

7 Selection Problems114

1．Selecting the Best of Several Normal Means with Independent Samples from Populations with a Com-mon Variance115

2．Selecting the Best of Several Normal Variances119

3．Selecting the Best of Several Binomial Proportions122

4．Selecting the Best of Several Exponential Scale Pa-rameters126

8 Sequential Sampling129

1．Sequential Tests of Hypotheses About Normal Means132

2．Sequential Tests of Hypotheses About Normal Vari-ances136

3．Sequential Tests of Hypotheses About Binomial Pro-portions140

4．Sequential Tests of Hypotheses About Exponential Scale Parameters143

9 Lot Acceptance Sampling Plans147

1．Military Standard 105 C150

2．Military Standard 414156

10 Sample-Size Precision Schedules163

1．Case Example:An Estimation Problem166

2．Case Example:A Test of Hypothesis167

3．Case Example:A Selection Problem171

11 Decision-Function Approach174

1．Estimating a Mean with Losses Proportional to the Square of the Error in the Estimate177

2．Estimating a Normal Mean with Losses Proportional to the Absolute Value of the Error in the Estimate178

3．Selecting the Best of Several Normal Means with In-dependent Samples from Populations with a Com-mon Variance180

4．Selecting the Better of Two Binomial Proportions182

5．Testing a Hypothesis About a Normal Mean with Loss from Acceptance and Loss from Rejection Linear Functions of the True but Unknown Population Mean185

6．Testing a Hypothesis About a Binomial Proportion with Loss from Acceptance and Loss from Rejection Linear Functions of the True but Unknown Binomial Proportion187

References190

Appendix Tables193

TABLE 1．Upper Percentage Points of the t Distribution195

TABLE 2．Upper Percentage Points of the x2 Distribu-tion196

TABLE 3．Upper 10 Percentage Points of the F Distri-bution198

TABLE 4．Upper 5 Percentage Points of the F Distri-bution200

TABLE 5．Upper 1 Percentage Points of the F Distri-bution202

TABLE 6．Upper Percentage Points of the Noncentral t Distribution when the Probability of Erroneously Reject-ing the Test Hypothesis(α)Equals 0．05204

TABLE 7．Upper Percentage Points of the Noncentral t Distribution when the Probability of Erroneously Reject-ing the Test Hypothesis(α)Equals 0．01205

TABLE 8．Upper Percentage Points of the Noncentral x2 Distribution when the Probability of Erroneously Re-jecting the Test Hypothesis(α)Equals 0．05206

TABLE 9．Upper Percentage Points of the Noncentral x2 Distribution when the Probability of Erroneously Re-jecting the Test Hypothesis(α)Equals 0．01207

TABLE 10．Upper 20 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．05208

TABLE 11．Upper 20 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．01209

TABLE 12．Upper 30 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．05210

TABLE 13．Upper 30 Percentage Points of the Ф Func-tion when the Probability of Erroneously Rejecting the Test Hypothesis(α)Equals 0．01211

TABLE 14．Upper 5 Percentage Points of the Multi-variate t Distribution with Correlations Plus One Half212

TABLE 15．Upper 1 Percentage Points of the Multi-variate t Distribution with Correlations Plus One Half213

TABLE 16．Upper 10 Percentage Points of the Student-ized Range,(xn－x1)/s214

TABLE 17．Upper 5 Percentage Points of the Student-ized Range,(xn－x1)/s216

TABLE 18．Upper 1 Percentage Points of the Student-ized Range,(xn－x1)/s218

TABLE 19．Upper Percentage Points of d(n,the Maxi-mum Absolute Difference Between Sample and Popula-tion Cumulative Distributions220

TABLE 20．y=2 arcsin ？221

Index223