Probability and statistics for engineers and scientists

ii This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does no[.]

This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest ii ■ Probability and Statistics for Engineers and Scientists i This page intentionally left blank ■ Probability and Statistics for Engineers and Scientists FOURTH EDITION Anthony Hayter University of Denver Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States iii INDEX standard deviations, 282 definition of, 104 of random variables, 104 of sample proportions (standard errors), 311 in standard normal distributions, 217 in z-tests, 375–377 standard errors of sample means, 313 of sample proportions, 311 in simple linear regression, 571 standardized random variables, 222, 223 standardized residuals, 638 standard normal distributions, 217–222 cumulative distribution function of, 787–788 state spaces (sample spaces), statistical estimation See estimation statistical inference, 267, 268 guide to methodologies for, 331–332 statistical process control (SPC), 736–742 acceptance sampling distinguished from, 758 control charts for, 736–738, 740–741 control limits for, 738–740 statistics definition of, 298 parameters distinguished from, 296 point estimates of, 297–298 stochastic processes, 193 studentized range distribution, critical points for, 794 success probability, point estimate of, 302 sum of squares partitioning in randomized block designs, 527 total, 499–506 simple linear regression and, 579–584 in three-factor experiments, 681–683 in two-factor experiments, 661–664 in variance, 282 sum of squares for error (SSE) in multiple linear regression, 612 in simple linear regression, 500–501 sum of squares for factor A and factor B, 663 sum of squares for interactions, 663 sum of squares for regression (SSR), 580 sum of squares for treatments (SST), 500 in analysis of variance tables, 507 symmetric binomial distributions, 151 symmetric distributions signed rank test of, 712 sign test of, 703 symmetric random variables, 97–98 symmetry, in histograms, 278 system reliability, 766–772 for complex systems, 769–771 for components in parallel, 768–769 for components in series, 767–768 t-distribution, 255–257 critical points for, 790 three-factor experiments, 679–687 time to failure, 772–774 t-intervals, 333–334 one-sided, 344, 345 two-sided, 335, 337–338 total probability, law of, 50–51 total quality management, 736 total sum of squares partitioning in one-factor analysis of variance, 499–506 in randomized block designs, 525–528 in simple linear regression, 501–506, 579–584 in two-factor experiments, 662 transformations of variables, 590–593 treatment sum of squares (SST) in analysis of variance tables, 507 in one-factor analysis of variance, 499–500 in randomized block designs, 526 trimmed means, 282 as unbiased estimate, 303 t-statistic, 315 for one-sided hypothesis testing, 359–365 for two-sided hypothesis testing, 354–358 t-tests deciding between z-tests and, 381–383 one-sided, 359–365 summary of, 382 two-sided, 356–358 Tukey intervals, 514 two-factor experiments, 650–677 analysis of variance tables for, 661–670 experimental design for, 650–653 modeling procedures and residual analysis for, 673–677 models for, 653–661 pairwise comparisons of factor level means, 670–673 2k experiments, 687–690 two-sample problems comparing two population means, 389–394 paired samples versus independent samples in, 394–397 two-sample t-tests, 402 general procedure, 423 with equal variances, 409 with unequal variances, 405–406 pooled variance procedure, 424 two-sample z-tests, 402, 410–411 two-sided confidence intervals, for population proportions, 435 two-sided hypothesis testing, 354–358 for population proportions, 441–445 significance levels for, 366–368 z-tests for, 376 825 two-sided t-intervals, 334, 335, 337–338 two-sided t-tests, 356–358 two-sided z-intervals, 346 two-sided z-tests, 376 two-way classifications, 478–480 two-way contingency tables, 478–486 Type I errors, 365 Type II errors, 365 power levels and, 374–375 unbalanced data sets, 494 unbalanced experimental designs, 675 unbiased estimates, 301–305 uncertainty, uniform distributions, 186–189 definition of, 186–188 examples of, 188–189 unimodal histograms, 278 unions of events, 18–21 definition of, 18 examples of, 21–28 of mutually exclusive events, 30 of three events, 29 upper control limit (UCL), 738 upper quartile, 110 variable control charts, 742–752 R-charts, 744–745 X¯ -charts, 743–745 variables association and causality between, 596–597 in multiple linear regression, multicolinearity of, 637–638 simple linear regression of relationships among, 543 transformations of, in simple linear regression, 590–593 See also random variables variance, 282–284 covariance and, 123–127 definition of, 103 minimum variance estimates of, 305–309 population variance, point estimate of, 304 of random variables, 102–112 calculation of, 104–107 Chebyshev’s inequality, 107–109 definition and interpretation of, 102–104 quantiles of, 109–112 sample variance, 314–315 See also analysis of variance Venn diagrams, Weibull, Ernst Hjalmar Waloddi, 205 Weibull distributions, 204–208 definition of, 204–206 examples of, 206–208 for hazard rates, 776 for modeling failure rates, 774 826 INDEX Whitney, Hassler, 721 Wilcoxon, 721 Wilcoxon one-sample test procedure (signed rank test), 709–715 Wilcoxon rank sum test, 721–724 X¯ -charts, 743–744 modifications of, 745 z-intervals, 346 z-tests, 375–378 deciding between t-tests and, 381–383 summary of, 383 two-sample, 410–411 ... keyword for materials in your areas of interest ii ■ Probability and Statistics for Engineers and Scientists i This page intentionally left blank ■ Probability and Statistics for Engineers and Scientists. .. iii INDEX standard deviations, 282 definition of, 104 of random variables, 104 of sample proportions (standard errors), 311 in standard normal distributions, 217 in z-tests, 375–377 standard errors... squares for error (SSE) in multiple linear regression, 612 in simple linear regression, 500–501 sum of squares for factor A and factor B, 663 sum of squares for interactions, 663 sum of squares for