Page 19 - Applied statistics and probability for engineers

Contents xv

7-2 Sampling Distributions 9-1.3 One-Sided and Two-Sided
and the Central Limit Theorem 241 Hypotheses 313
7-3 General Concepts of Point Estimation 249 9-1.4 P-Values in Hypothesis Tests 314
7-3.1 Unbiased Estimators 249 9-1.5 Connection Between Hypothesis Tests
7-3.2 Variance of a Point Estimator 251 and Conidence Intervals 316
7-3.3 Standard Error: Reporting a Point 9-1.6 General Procedure for Hypothesis
Estimate 251 Tests 318
7.3.4 Bootstrap Standard Error 252 9-2 Tests on the Mean of a Normal Distribution,
7-3.5 Mean Squared Error of an Estimator 254 Variance Known 322
7-4 Methods of Point Estimation 256 9-2.1 Hypothesis Tests on the Mean 322
7-4.1 Method of Moments 256 9-2.2 Type II Error and Choice of Sample
7-4.2 Method of Maximum Likelihood 258 Size 325
7-4.3 Bayesian Estimation of 9-2.3 Large-Sample Test 329
Parameters 264 9-3 Tests on the Mean of a Normal Distribution,
Variance Unknown 331
Chapter 8 Statistical Intervals for a
9-3.1 Hypothesis Tests on the Mean 331
Single Sample 271
9-3.2 Type II Error and Choice of Sample
8-1 Conidence Interval on the Mean of a Normal Size 336
Distribution, Variance Known 273 9-4 Tests on the Variance and Standard
8-1.1 Development of the Conidence Interval Deviation of a Normal Distribution 340
and Its Basic Properties 273 9-4.1 Hypothesis Tests on the Variance 341
8-1.2 Choice of Sample Size 276 9-4.2 Type II Error and Choice of Sample
8-1.3 One-Sided Conidence Bounds 277 Size 343
8-1.4 General Method to Derive a Conidence 9-5 Tests on a Population Proportion 344
Interval 277 9-5.1 Large-Sample Tests on a Proportion 344
8-1.5 Large-Sample Conidence Interval 9-5.2 Type II Error and Choice of Sample
for μ 279 Size 347
8-2 Conidence Interval on the Mean of a Normal 9-6 Summary Table of Inference Procedures
Distribution, Variance Unknown 282 for a Single Sample 350
8-2.1 t Distribution 283 9-7 Testing for Goodness of Fit 350
8-2.2 t Conidence Interval on μ 284 9-8 Contingency Table Tests 354
8-3 Conidence Interval on the Variance and 9-9 Nonparametric Procedures 357
Standard Deviation of a Normal 9-9.1 The Sign Test 358
Distribution 287 9-9.2 The Wilcoxon Signed-Rank Test 362
8-4 Large-Sample Conidence Interval 9-9.3 Comparison to the t-Test 364
for a Population Proportion 291 9-10 Equivalence Testing 365
8-5 Guidelines for Constructing Conidence 9-11 Combining P-Values 367
Intervals 296
Chapter 10 Statistical Inference for
8.6 Bootstrap Conidence Interval 296
Two Samples 373
8-7 Tolerance and Prediction Intervals 297
8-7.1 Prediction Interval for a Future 10-1 Inference on the Difference in Means of Two
Observation 297 Normal Distributions, Variances Known 374
8-7.2 Tolerance Interval for a Normal 10-1.1 Hypothesis Tests on the Difference in
Distribution 298 Means, Variances Known 376
10-1.2 Type II Error and Choice of Sample
Chapter 9 Tests of Hypotheses for a Size 377
Single Sample 305 10-1.3 Conidence Interval on the Difference in
Means, Variances Known 379
9-1 Hypothesis Testing 306
10-2 Inference on the Difference in Means of two
9-1.1 statistical hypotheses 306
Normal Distributions, Variances Unknown 383
9-1.2 Tests of Statistical Hypotheses 308