Statistics for engineering and the sciences / William Mendenhall and Terry Sincich

This text is designed for a two-semester introductory course in statistics for students majoring in engineering or any of the physical sciences. Inevitably, once these students graduate and are employed, they will be involved in the collection and analysis of data and will be required to think critically about the results. Consequently, they need to acquire knowledge of the basic concepts of data description and statistical inference and familiarity with statistical methods they are required to use on the job.

Preface	p. ix
Chapter 1 Introduction	p. 1
1.1 Statistics: The Science of Data	p. 2
1.2 Fundamental Elements of Statistics	p. 2
1.3 Types of Data	p. 5
1.4 The Role of Statistics in Critical Thinking	p. 7
1.5 A Guide to Statistical Methods Presented in This Text	p. 9
Statistics in Action: Contamination of Fish in the Tennessee River: Collecting the Data	p. 10
Chapter 2 Descriptive Statistics	p. 12
2.1 Graphical and Numerical Methods for Describing Qualitative Data	p. 13
2.2 Graphical Methods for Describing Quantitative Data	p. 19
2.3 Numerical Methods for Describing Quantitative Data	p. 27
2.4 Measures of Central Tendency	p. 28
2.5 Measures of Variation	p. 32
2.6 Measures of Relative Standing	p. 38
2.7 Methods for Detecting Outliers	p. 41
2.8 Distorting the Truth with Descriptive Statistics	p. 45
Statistics in Action: Characteristics of Contaminated Fish in the Tennessee River, Alabama	p. 56
Chapter 3 Probability	p. 59
3.1 The Role of Probability in Statistics	p. 60
3.2 Events, Sample Spaces, and Probability	p. 60
3.3 Compound Events	p. 70
3.4 Complementary Events	p. 72
3.5 Conditional Probability	p. 76
3.6 Probability Rules for Unions and Intersections	p. 80
3.7 Bayes' Rule (Optional)	p. 90
3.8 Some Counting Rules	p. 93
3.9 Probability and Statistics: An Example	p. 103
3.10 Random Sampling	p. 105
Statistics in Action: Assessing Predictors of Software Defects in NASA Spacecraft Instrument Code	p. 114
Chapter 4 Discrete Random Variables	p. 117
4.1 Discrete Random Variables	p. 118
4.2 The Probability Distribution for a Discrete Random Variable	p. 118
4.3 Expected Values for Random Variables	p. 123
4.4 Some Useful Expectation Theorems	p. 127
4.5 Bernoulli Trials	p. 129
4.6 The Binomial Probability Distribution	p. 130
4.7 The Multinomial Probability Distribution	p. 137
4.8 The Negative Binomial and the Geometric Probability Distributions	p. 142
4.9 The Hypergeometric Probability Distribution	p. 146
4.10 The Poisson Probability Distribution	p. 151
4.11 Moments and Moment Generating Functions (Optional)	p. 157
Statistics in Action: The Reliability of a "One-Shot" Device	p. 165
Chapter 5 Continuous Random Variables	p. 168
5.1 Continuous Random Variables	p. 169
5.2 The Density Function for a Continuous Random Variable	p. 170
5.3 Expected Values for Continuous Random Variables	p. 172
5.4 The Uniform Probability Distribution	p. 177
5.5 The Normal Probability Distribution	p. 180
5.6 Descriptive Methods for Assessing Normality	p. 184
5.7 Gamma-Type Probability Distributions	p. 190
5.8 The Weibull Probability Distribution	p. 194
5.9 Beta-Type Probability Distributions	p. 197
5.10 Moments and Moment Generating Functions (Optional)	p. 200
Statistics in Action: Super Weapons Development-Optimizing the Hit Ratio	p. 206
Chapter 6 Bivariate Probability Distributions and Sampling Distributions	p. 211
6.1 Bivariate Probability Distributions for Discrete Random Variables	p. 212
6.2 Bivariate Probability Distributions for Continuous Random Variables	p. 217
6.3 The Expected Value of Functions of Two Random Variables	p. 221
6.4 Independence	p. 223
6.5 The Covariance and Correlation of Two Random Variables	p. 225
6.6 Probability Distributions and Expected Values of Functions of Random Variables (Optional)	p. 228
6.7 Sampling Distributions	p. 236
6.8 Approximating a Sampling Distribution by Monte Carlo Simulation	p. 237
6.9 The Sampling Distributions of Means and Sums	p. 240
6.10 Normal Approximation to the Binomial Distribution	p. 245
6.11 Sampling Distributions Related to the Normal Distribution	p. 248
Statistics in Action: Availability of an Up/Down Maintained System	p. 259
Chapter 7 Estimation Using Confidence Intervals	p. 262
7.1 Point Estimators and their Properties	p. 263
7.2 Finding Point Estimators: Classical Methods of Estimation	p. 267
7.3 Finding Interval Estimators: The Pivotal Method	p. 274
7.4 Estimation of a Population Mean	p. 281
7.5 Estimation of the Difference Between Two Population Means: Independent Samples	p. 287
7.6 Estimation of the Difference Between Two Population Means: Matched Pairs	p. 294
7.7 Estimation of a Population Proportion	p. 299
7.8 Estimation of the Difference Between Two Population Proportions	p. 302
7.9 Estimation of a Population Variance	p. 305
7.10 Estimation of the Ratio of Two Population Variances	p. 309
7.11 Choosing the Sample Size	p. 315
7.12 Alternative Interval Estimation Methods: Bootstrapping and Bayesian Methods (Optional)	p. 318
Statistics in Action: Bursting Strength of PET Beverage Bottles	p. 332
Chapter 8 Tests of Hypotheses	p. 335
8.1 The Relationship Between Statistical Tests of Hypotheses and Confidence Intervals	p. 336
8.2 Elements and Properties of a Statistical Test	p. 336
8.3 Finding Statistical Tests: Classical Methods	p. 342
8.4 Choosing the Null and Alternative Hypotheses	p. 346
8.5 Testing a Population Mean	p. 348
8.6 The Observed Significance Level for a Test	p. 354
8.7 Testing the Difference Between Two Population Means: Independent Samples	p. 357
8.8 Testing the Difference Between Two Population Means: Matched Pairs	p. 364
8.9 Testing a Population Proportion	p. 369
8.10 Testing the Difference Between Two Population Proportions	p. 372
8.11 Testing a Population Variance	p. 376
8.12 Testing the Ratio of Two Population Variances	p. 379
8.13 Alternative Testing Procedures: Bootstrapping and Bayesian Methods (Optional)	p. 383
Statistics in Action: Comparing Methods for Dissolving Drug Tablets-Dissolution Method Equivalence Testing	p. 395
Chapter 9 Categorical Data Analysis	p. 400
9.1 Categorical Data and Multinomial Probabilities	p. 401
9.2 Estimating Category Probabilities in a One-Way Table	p. 401
9.3 Testing Category Probabilities in a One-Way Table	p. 405
9.4 Inferences About Category Probabilities in a Two-Way (Contingency) Table	p. 409
9.5 Contingency Tables with Fixed Marginal Totals	p. 417
9.6 Exact Tests for Independence in a Contingency Table Analysis (Optional)	p. 422
Statistics in Action: The Public's Perception of Engineers and Engineering	p. 432
Chapter 10 Simple Linear Regression	p. 439
10.1 Regression Models	p. 440
10.2 Model Assumptions	p. 441
10.3 Estimating [beta subscript 0] and [beta subscript 1]: The Method of Least Squares	p. 443
10.4 Properties of the Least Squares Estimators	p. 454
10.5 An Estimator of [sigma superscript 2]	p. 456
10.6 Assessing the Utility of the Model: Making Inferences About the Slope [beta subscript 1]	p. 460
10.7 The Coefficient of Correlation	p. 465
10.8 The Coefficient of Determination	p. 469
10.9 Using the Model for Estimation and Prediction	p. 473
10.10 A Complete Example	p. 480
10.11 A Summary of the Steps to Follow in Simple Linear Regression	p. 483
Statistics in Action: Can Dowsers Really Detect Water?	p. 491
Chapter 11 Multiple Regression Analysis	p. 495
11.1 General Form of a Multiple Regression Model	p. 496
11.2 Model Assumptions	p. 497
11.3 Fitting the Model: The Method of Least Squares	p. 498
11.4 Computations Using Matrix Algebra: Estimating and Making Inferences About the Individual [beta] Parameters	p. 499
11.5 Assessing Overall Model Adequacy	p. 506
11.6 A Confidence Interval for E(y) and a Prediction Interval for a Future Value of y	p. 510
11.7 A First-Order Model with Quantitative Predictors	p. 519
11.8 An Interaction Model with Quantitative Predictors	p. 528
11.9 A Quadratic (Second-Order) Model with a Quantitative Predictor	p. 533
11.10 Checking Assumptions: Residual Analysis	p. 540
11.11 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation	p. 559
11.12 A Summary of the Steps to Follow in a Multiple Regression Analysis	p. 568
Statistics in Action: Bid-Rigging in the Highway Construction Industry	p. 575
Chapter 12 Model Building	p. 583
12.1 Introduction: Why Model Building Is Important	p. 584
12.2 The Two Types of Independent Variables: Quantitative and Qualitative	p. 585
12.3 Models with a Single Quantitative Independent Variable	p. 586
12.4 Models with Two Quantitative Independent Variables	p. 593
12.5 Coding Quantitative Independent Variables (Optional)	p. 600
12.6 Models with One Qualitative Independent Variable	p. 605
12.7 Models with Both Quantitative and Qualitative Independent Variables	p. 611
12.8 Tests for Comparing Nested Models	p. 621
12.9 External Model Validation (Optional)	p. 628
12.10 Stepwise Regression	p. 630
Statistics in Action: Deregulation of the Intrastate Trucking Industry	p. 640
Chapter 13 Principles of Experimental Design	p. 648
13.1 Introduction	p. 649
13.2 Experimental Design Terminology	p. 649
13.3 Controlling the Information in an Experiment	p. 651
13.4 Noise-Reducing Designs	p. 652
13.5 Volume-Increasing Designs	p. 658
13.6 Selecting the Sample Size	p. 663
13.7 The Importance of Randomization	p. 665
Statistics in Action: Anticorrosive Behavior of Epoxy Coatings Augmented with Zinc	p. 668
Chapter 14 The Analysis of Variance for Designed Experiments	p. 671
14.1 Introduction	p. 672
14.2 The Logic Behind an Analysis of Variance	p. 672
14.3 One-Factor Completely Randomized Designs	p. 674
14.4 Randomized Block Designs	p. 685
14.5 Two-Factor Factorial Experiments	p. 698
14.6 More Complex Factorial Designs (Optional)	p. 714
14.7 Nested Sampling Designs (Optional)	p. 721
14.8 Multiple Comparisons of Treatment Means	p. 732
14.9 Checking ANOVA Assumptions	p. 739
Statistics in Action: On the Trail of the Cockroach	p. 751
Chapter 15 Nonparametric Statistics	p. 755
15.1 Introduction: Distribution-Free Tests	p. 756
15.2 Testing for Location of a Single Population	p. 757
15.3 Comparing Two Populations: Independent Random Samples	p. 762
15.4 Comparing Two Populations: Matched-Pairs Design	p. 769
15.5 Comparing Three or More Populations: Completely Randomized Design	p. 775
15.6 Comparing Three or More Populations: Randomized Block Design	p. 780
15.7 Nonparametric Regression	p. 784
Statistics in Action: Deadly Exposure: Agent Orange and Vietnam Vets	p. 796
Chapter 16 Statistical Process and Quality Control	p. 800
16.1 Total Quality Management	p. 801
16.2 Variable Control Charts	p. 801
16.3 Control Chart for Means: x-Chart	p. 806
16.4 Control Chart for Process Variation: R-Chart	p. 814
16.5 Detecting Trends in a Control Chart: Runs Analysis	p. 819
16.6 Control Chart for Percent Defectives: p-Chart	p. 821
16.7 Control Chart for the Number of Defectives per Item: c-Chart	p. 825
16.8 Tolerance Limits	p. 829
16.9 Capability Analysis (Optional)	p. 832
16.10 Acceptance Sampling for Defectives	p. 839
16.11 Other Sampling Plans (Optional)	p. 844
16.12 Evolutionary Operations (Optional)	p. 845
Statistics in Action: Testing Jet Fuel Additive for Safety	p. 851
Chapter 17 Product and System Reliability	p. 857
17.1 Introduction	p. 858
17.2 Failure Time Distributions	p. 858
17.3 Hazard Rates	p. 859
17.4 Life Testing: Censored Sampling	p. 863
17.5 Estimating the Parameters of an Exponential Failure Time Distribution	p. 864
17.6 Estimating the Parameters of a Weibull Failure Time Distribution	p. 867
17.7 System Reliability	p. 872
Statistics in Action: Modeling the Hazard Rate of Reinforced Concrete Bridge Deck Deterioration	p. 879
Appendix A Matrix Algebra	p. 882
A.1 Matrices and Matrix Multiplication	p. 882
A.2 Identity Matrices and Matrix Inversion	p. 886
A.3 Solving Systems of Simultaneous Linear Equations	p. 889
A.4 A Procedure for Inverting a Matrix	p. 891
Appendix B Useful Statistical Tables	p. 896
Table 1 Random Numbers	p. 897
Table 2 Cumulative Binomial Probabilities	p. 901
Table 3 Exponentials	p. 905
Table 4 Cumulative Poisson Probabilities	p. 906
Table 5 Normal Curve Areas	p. 908
Table 6 Gamma Function	p. 909
Table 7 Critical Values for Student's T	p. 910
Table 8 Critical Values of x[superscript 2]	p. 911
Table 9 Percentage Points of the F Distribution, [alpha] = .10	p. 913
Table 10 Percentage Points of the F Distribution, [alpha] = .05	p. 915
Table 11 Percentage Points of the F Distribution, [alpha] = .025	p. 917
Table 12 Percentage Points of the F Distribution, [alpha] = .01	p. 919
Table 13 Percentage Points of the Studentized Range q(p,v), [alpha] = .05	p. 921
Table 14 Percentage Points of the Studentized Range q(p,v), [alpha] = .01	p. 923
Table 15 Critical Values of T[subscript L] and T[subscript U] for the Wilcoxon Rank Sum Test: Independent Samples	p. 925
Table 16 Critical Values of T[subscript 0] for the Wilcoxon Matched-Pairs Signed Rank Test	p. 926
Table 17 Critical Values of Spearman's Rank Correlation Coefficient	p. 927
Table 18 Critical Values of C for the Theil Zero-Slope Test	p. 928
Table 19 Factors Used When Constructing Control Charts	p. 932
Table 20 Values of K for Tolerance Limits for Normal Distributions	p. 933
Table 21 Sample Size n for Nonparametric Tolerance Limits	p. 934
Table 22 Sample Size Code Letters: MIL-STD-105D	p. 934
Table 23 A Portion of the Master Table for Normal Inspection (Single Sampling): MIL-STD-105D	p. 935
Appendix C SAS for Windows Tutorial	p. 936
Appendix D MINITAB for Windows Tutorial	p. 965
Appendix E SPSS for Windows Tutorial	p. 998
References	p. 1028
Selected Short Answers	p. 1036
Credits	p. 1049
Index	p. 1054

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