Probability and Statistics for Engineering and the Sciences: Enhanced (7th Edition)

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 8
Introduction......Page 18
1.1 Populations, Samples, and Processes......Page 19
Branches of Statistics......Page 20
Enumerative Versus Analytic Studies......Page 23
Collecting Data......Page 24
Stem-and-Leaf Displays......Page 27
Dotplots......Page 29
Histograms......Page 30
Histogram Shapes......Page 35
Qualitative Data......Page 36
Multivariate Data......Page 37
1.3 Measures of Location......Page 41
The Mean......Page 42
The Median......Page 43
Other Measures of Location: Quartiles, Percentiles, and Trimmed Means......Page 45
Categorical Data and Sample Proportions......Page 46
1.4 Measures of Variability......Page 48
Measures of Variability for Sample Data......Page 49
Motivation for s[sup(2)]......Page 50
A Computing Formula for s[sup(2)]......Page 51
Boxplots......Page 52
Boxplots That Show Outliers......Page 53
Comparative Boxplots......Page 54
Supplementary Exercises......Page 59
Bibliography......Page 62
Introduction......Page 63
The Sample Space of an Experiment......Page 64
Events......Page 65
Some Relations from Set Theory......Page 66
2.2 Axioms, Interpretations, and Properties of Probability......Page 68
Interpreting Probability......Page 70
More Probability Properties......Page 71
Determining Probabilities Systematically......Page 73
Equally Likely Outcomes......Page 74
2.3 Counting Techniques......Page 76
The Product Rule for Ordered Pairs......Page 77
A More General Product Rule......Page 78
Permutations and Combinations......Page 79
2.4 Conditional Probability......Page 84
The Definition of Conditional Probability......Page 85
The Multiplication Rule for P(A ∩ B)......Page 86
Bayes’ Theorem......Page 89
2.5 Independence......Page 93
The Multiplication Rule for P(A ∩ B)......Page 94
Independence of More Than Two Events......Page 96
Supplementary Exercises......Page 99
Bibliography......Page 102
Introduction......Page 103
3.1 Random Variables......Page 104
Two Types of Random Variables......Page 106
3.2 Probability Distributions for Discrete Random Variables......Page 107
A Parameter of a Probability Distribution......Page 111
The Cumulative Distribution Function......Page 112
3.3 Expected Values......Page 117
The Expected Value of X......Page 118
The Expected Value of a Function......Page 120
The Variance of X......Page 121
A Shortcut Formula for σ2......Page 122
Rules of Variance......Page 123
3.4 The Binomial Probability Distribution......Page 125
The Binomial Random Variable and Distribution......Page 127
Using Binomial Tables*......Page 128
The Mean and Variance of X......Page 130
The Hypergeometric Distribution......Page 133
The Negative Binomial Distribution......Page 135
3.6 The Poisson Probability Distribution......Page 138
The Poisson Distribution as a Limit......Page 139
The Mean and Variance of X......Page 140
The Poisson Process......Page 141
Supplementary Exercises......Page 143
Bibliography......Page 146
Introduction......Page 147
Probability Distributions for Continuous Variables......Page 148
The Cumulative Distribution Function......Page 153
Using F(x) to Compute Probabilities......Page 154
Percentiles of a Continuous Distribution......Page 156
Expected Values......Page 158
4.3 The Normal Distribution......Page 161
The Standard Normal Distribution......Page 162
Percentiles of the Standard Normal Distribution......Page 164
z[sub(α)] Notation......Page 165
Nonstandard Normal Distributions......Page 166
Percentiles of an Arbitrary Normal Distribution......Page 168
Approximating the Binomial Distribution......Page 169
The Exponential Distribution......Page 174
The Gamma Function......Page 176
The Gamma Distribution......Page 177
The Chi-Squared Distribution......Page 178
The Weibull Distribution......Page 180
The Lognormal Distribution......Page 183
The Beta Distribution......Page 184
Sample Percentiles......Page 187
A Probability Plot......Page 188
Beyond Normality......Page 193
Supplementary Exercises......Page 196
Bibliography......Page 200
Introduction......Page 201
Two Discrete Random Variables......Page 202
Two Continuous Random Variables......Page 203
Independent Random Variables......Page 206
More Than Two Random Variables......Page 208
Conditional Distributions......Page 210
5.2 Expected Values, Covariance, and Correlation......Page 213
Covariance......Page 215
Correlation......Page 217
5.3 Statistics and Their Distributions......Page 219
Random Samples......Page 221
Deriving a Sampling Distribution......Page 222
Simulation Experiments......Page 225
The Case of a Normal Population Distribution......Page 230
The Central Limit Theorem......Page 232
Other Applications of the Central Limit Theorem......Page 234
5.5 The Distribution of a Linear Combination......Page 236
The Case of Normal Random Variables......Page 237
Supplementary Exercises......Page 241
Bibliography......Page 243
Introduction......Page 244
6.1 Some General Concepts of Point Estimation......Page 245
Unbiased Estimators......Page 248
Estimators with Minimum Variance......Page 252
Some Complications......Page 253
Reporting a Point Estimate: The Standard Error......Page 255
The Method of Moments......Page 260
Maximum Likelihood Estimation......Page 262
Estimating Functions of Parameters......Page 265
Some Complications......Page 266
Supplementary Exercises......Page 269
Bibliography......Page 270
Introduction......Page 271
7.1 Basic Properties of Confidence Intervals......Page 272
Interpreting a Confidence Interval......Page 274
Other Levels of Confidence......Page 275
Confidence Level, Precision, and Sample Size......Page 276
Deriving a Confidence Interval......Page 277
Bootstrap Confidence Intervals......Page 278
A Large-Sample Interval for μ......Page 280
A Confidence Interval for a Population Proportion......Page 282
One-Sided Confidence Intervals (Confidence Bounds)......Page 284
Properties of t Distributions......Page 287
The One-Sample t Confidence Interval......Page 289
A Prediction Interval for a Single Future Value......Page 291
Tolerance Intervals......Page 292
Intervals Based on Nonnormal Population Distributions......Page 293
7.4 Confidence Intervals for the Variance and Standard Deviation of a Normal Population......Page 295
Supplementary Exercises......Page 298
Bibliography......Page 300
Introduction......Page 301
8.1 Hypotheses and Test Procedures......Page 302
Test Procedures......Page 303
Errors in Hypothesis Testing......Page 304
Case I: A Normal Population with Known σ......Page 311
Case II: Large-Sample Tests......Page 316
Case III: A Normal Population Distribution......Page 317
Large-Sample Tests......Page 323
Small-Sample Tests......Page 326
8.4 P-Values......Page 328
P-Values for z Tests......Page 331
P-Values for t Tests......Page 332
8.5 Some Comments on Selecting a Test......Page 335
Statistical Versus Practical Significance......Page 336
The Likelihood Ratio Principle......Page 337
Supplementary Exercises......Page 338
Bibliography......Page 341
Introduction......Page 342
9.1 z Tests and Confidence Intervals for a Difference Between Two Population Means......Page 343
Test Procedures for Normal Populations with Known Variances......Page 344
Using a Comparison to Identify Causality......Page 345
β and the Choice of Sample Size......Page 346
Large-Sample Tests......Page 348
Confidence Intervals for μ[sub(1)] – μ[sub(2)]......Page 349
9.2 The Two-Sample t Test and Confidence Interval......Page 353
Pooled t Procedures......Page 356
Type II Error Probabilities......Page 357
9.3 Analysis of Paired Data......Page 361
The Paired t Test......Page 362
A Confidence Interval for μD......Page 364
Paired Versus Unpaired Experiments......Page 366
9.4 Inferences Concerning a Difference Between Population Proportions......Page 370
A Large-Sample Test Procedure......Page 371
Type II Error Probabilities and Sample Sizes......Page 372
A Large-Sample Confidence Interval for p[sub(1)] – p[sub(2)]......Page 374
Small-Sample Inferences......Page 375
The F Distribution......Page 377
Inferential Methods......Page 378
P-Values for F Tests......Page 379
A Confidence Interval for σ[sub(1)]/σ[sub(2)]......Page 380
Supplementary Exercises......Page 381
Bibliography......Page 385
Introduction......Page 386
10.1 Single-Factor ANOVA......Page 387
Notation and Assumptions......Page 389
The Test Statistic......Page 390
F Distributions and the F Test......Page 391
Sums of Squares......Page 392
10.2 Multiple Comparisons in ANOVA......Page 396
Tukey’s Procedure (the T Method)......Page 397
The Interpretation of α in Tukey’s Method......Page 400
Confidence Intervals for Other Parametric Functions......Page 401
The ANOVA Model......Page 402
β for the F Test......Page 404
Unequal Sample Sizes......Page 406
A Random Effects Model......Page 408
Supplementary Exercises......Page 412
Bibliography......Page 413
Introduction......Page 414
11.1 Two-Factor ANOVA with K[sub(ij)] = 1......Page 415
The Fixed Effects Model......Page 416
Test Procedures......Page 418
Expected Mean Squares......Page 420
Randomized Block Experiments......Page 421
Models for Random Effects......Page 424
11.2 Two-Factor ANOVA with K[sub(ij) > 1......Page 427
Parameters and Hypotheses for the Fixed Effects Model......Page 428
The Model and Test Procedures......Page 429
Multiple Comparisons......Page 432
Models with Mixed and Random Effects......Page 433
11.3 Three-Factor ANOVA......Page 436
The Three-Factor Fixed Effects Model......Page 437
Analysis of a Three-Factor Experiment......Page 438
Latin Square Designs......Page 441
2[sup(3)] Experiments......Page 446
2[sup(p)] Experiments for p > 3......Page 449
Confounding......Page 451
Confounding Using More Than Two Blocks......Page 452
Fractional Replication......Page 453
Supplementary Exercises......Page 459
Bibliography......Page 462
Introduction......Page 463
12.1 The Simple Linear Regression Model......Page 464
A Linear Probabilistic Model......Page 467
12.2 Estimating Model Parameters......Page 471
Estimating σ[sup(2)] and σ......Page 475
The Coefficient of Determination......Page 479
Terminology and Scope of Regression Analysis......Page 481
12.3 Inferences About the Slope Parameter β[sub(1)]......Page 485
A Confidence Interval for β[sub(1)]......Page 488
Hypothesis-Testing Procedures......Page 490
Regression and ANOVA......Page 492
12.4 Inferences Concerning μ[sub(y-x*)] and the Prediction of Future Y Values......Page 494
Inferences Concerning μ[sub(y.x*)]......Page 495
A Prediction Interval for a Future Value of Y......Page 498
The Sample Correlation Coefficient r......Page 502
Properties of r......Page 504
The Population Correlation Coefficient ρ and Inferences About Correlation......Page 505
Other Inferences Concerning ρ......Page 508
Supplementary Exercises......Page 511
Bibliography......Page 516
Introduction......Page 517
Residuals and Standardized Residuals......Page 518
Diagnostic Plots......Page 519
Difficulties and Remedies......Page 520
13.2 Regression with Transformed Variables......Page 525
More General Regression Methods......Page 530
Logistic Regression......Page 532
13.3 Polynomial Regression......Page 536
Estimation of Parameters Using Least Squares......Page 537
(omitted)[sup(2) and R2......Page 539
Statistical Intervals and Test Procedures......Page 540
Centering x Values......Page 541
13.4 Multiple Regression Analysis......Page 545
Models with Interaction and Quadratic Predictors......Page 546
Models with Predictors for Categorical Variables......Page 548
Estimating Parameters......Page 549
(omitted)[sup(2)] and R2......Page 551
A Model Utility Test......Page 553
Inferences in Multiple Regression......Page 554
Assessing Model Adequacy......Page 559
Transformations in Multiple Regression......Page 567
Standardizing Variables......Page 568
Variable Selection......Page 570
Identification of Influential Observations......Page 574
Multicollinearity......Page 576
Supplementary Exercises......Page 579
Bibliography......Page 584
Introduction......Page 585
14.1 Goodness-of-Fit Tests When Category Probabilities Are Completely Specified......Page 586
P-Values for Chi-Squared Tests......Page 589
X[sup(2)] When the pi’s Are Functions of Other Parameters......Page 590
X[sup(2)] When the Underlying Distribution Is Continuous......Page 591
X[sup(2)] When Parameters Are Estimated......Page 593
Goodness of Fit for Discrete Distributions......Page 597
Goodness of Fit for Continuous Distributions......Page 599
A Special Test for Normality......Page 601
14.3 Two-Way Contingency Tables......Page 604
Testing for Homogeneity......Page 605
Testing for Independence......Page 607
Supplementary Exercises......Page 612
Bibliography......Page 615
Introduction......Page 616
15.1 The Wilcoxon Signed-Rank Test......Page 617
A General Description of the Wilcoxon Signed-Rank Test......Page 619
Paired Observations......Page 620
A Large-Sample Approximation......Page 621
Efficiency of the Wilcoxon Signed-Rank Test......Page 623
Development of the Test When m = 3, n = 4......Page 625
General Description of the Wilcoxon Rank-Sum Test......Page 626
A Normal Approximation for W......Page 628
Efficiency of the Wilcoxon Rank-Sum Test......Page 629
The Wilcoxon Signed-Rank Interval......Page 631
The Wilcoxon Rank-Sum Interval......Page 633
The Kruskal–Wallis Test......Page 635
Friedman’s Test for a Randomized Block Experiment......Page 637
Supplementary Exercises......Page 639
Bibliography......Page 641
Introduction......Page 642
16.1 General Comments on Control Charts......Page 643
16.2 Control Charts for Process Location......Page 644
The X Chart Based on Known Parameter Values......Page 645
X Charts Based on Estimated Parameters......Page 646
Performance Characteristics of Control Charts......Page 649
Supplemental Rules for X Charts......Page 651
Robust Control Charts......Page 652
The S Chart......Page 654
The R Chart......Page 655
Charts Based on Probability Limits......Page 657
The ρ Chart for Fraction Defective......Page 658
The c Chart for Number of Defectives......Page 659
Control Charts Based on Transformed Data......Page 661
The V-Mask......Page 663
Computational Form of the CUSUM Procedure......Page 666
Equivalence of the V-Mask and Computational Form......Page 667
Designing a CUSUM Procedure......Page 669
16.6 Acceptance Sampling......Page 671
Single-Sampling Plans......Page 672
Designing a Single-Sample Plan......Page 673
Double-Sampling Plans......Page 675
Rectifying Inspection and Other Design Criteria......Page 676
Supplementary Exercises......Page 677
Bibliography......Page 678
Appendix Tables......Page 680
A.1 Cumulative Binomial Probabilities......Page 681
A.2 Cumulative Poisson Probabilities......Page 683
A.3 Standard Normal Curve Areas......Page 685
A.4 The Incomplete Gamma Function......Page 687
A.5 Critical Values for t Distributions......Page 688
A.6 Tolerance Critical Values for Normal Population Distributions......Page 689
A.7 Critical Values for Chi-Squared Distributions......Page 690
A.8 t Curve Tail Areas......Page 691
A.9 Critical Values for F Distributions......Page 693
A.10 Critical Values for Studentized Range Distributions......Page 699
A.11 Chi-Squared Curve Tail Areas......Page 700
A.12 Critical Values for the Ryan–Joiner Test of Normality......Page 702
A.13 Critical Values for the Wilcoxon Signed-Rank Test......Page 703
A.14 Critical Values for the Wilcoxon Rank-Sum Test......Page 704
A.15 Critical Values for the Wilcoxon Signed-Rank Interval......Page 705
A.16 Critical Values for the Wilcoxon Rank-Sum Interval......Page 706
A.17 β Curves for t Tests......Page 707
Answers to Selected Odd-Numbered Exercises......Page 708
Index......Page 727
Glossary of Symbols/Abbreviations for Chapters 1–16......Page 738
Sample Exams......Page 742