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[.]

Probability and Statistics for Engineers and

Scientists

i

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

of, 787–788

state spaces (sample spaces), 1

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

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

2kexperiments, 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

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, 2 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