Statistics and probability with applications for engineers and scientists

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Contents......Page 9
Chapter 1 Introduction......Page 27
  1.1.1 Motivation for the Study......Page 28
  1.1.3 Changing Criteria......Page 29
  1.1.4 A Summary of the Various Phases of the Investigation......Page 31
 1.3 An Observational Study......Page 32
 1.5 A Brief Description of What is Covered in this Book......Page 33
Chapter 2 Describing Data Graphically and Numerically......Page 39
  2.1.2 Population and Sample in a Statistical Study......Page 40
  2.2.1 Nominal Data......Page 44
  2.2.4 Ratio Data......Page 45
 2.3 Frequency Distribution Tables for Qualitative and Quantitative Data......Page 46
  2.3.1 Qualitative Data......Page 47
  2.3.2 Quantitative Data......Page 50
  2.4.1 Dot Plot......Page 56
  2.4.2 Pie Chart......Page 57
  2.4.3 Bar Chart......Page 59
  2.4.4 Histograms......Page 63
  2.4.5 Line Graph......Page 70
  2.4.6 Stem‐and‐Leaf Plot......Page 71
 2.5 Numerical Measures of Quantitative Data......Page 76
  2.5.1 Measures of Centrality......Page 77
  2.5.2 Measures of Dispersion......Page 82
  2.6.1 Mean of a Grouped Data......Page 93
  2.6.2 Median of a Grouped Data......Page 94
  2.6.4 Variance of a Grouped Data......Page 95
 2.7 Measures of Relative Position......Page 96
  2.7.1 Percentiles......Page 97
  2.7.3 Interquartile Range (IQR)......Page 98
  2.7.4 Coefficient of Variation......Page 99
  2.8.1 Construction of a Box Plot......Page 101
  2.8.2 How to Use the Box Plot......Page 102
 2.9 Measures of Association......Page 106
 2.10 Case Studies......Page 110
  2.10.1 About St. Luke's Hospital......Page 111
 2.11 Using JMP......Page 112
 2.11 Review Practice Problems......Page 113
 3.1 Introduction......Page 123
  3.2.1 Random Experiments and Sample Spaces......Page 124
  3.2.2 Events......Page 125
 3.3 Concepts of Probability......Page 129
  3.4.1 Tree Diagram......Page 134
  3.4.3 Combinations......Page 136
  3.4.4 Arrangements of n Objects Involving Several Kinds of Objects......Page 137
 3.5 Conditional Probability......Page 139
 3.6 Bayes's Theorem......Page 142
 3.7 Introducing Random Variables......Page 146
 3.7 Review Practice Problems......Page 148
Chapter 4 Discrete Random Variables and Some Important Discrete Probability Distributions......Page 154
 4.1 Graphical Descriptions of Discrete Distributions......Page 155
  4.2.1 Expected Value of Discrete Random Variables and Their Functions......Page 156
  4.2.2 The Moment‐Generating Function‐Expected Value of a Special Function of X......Page 159
 4.3 The Discrete Uniform Distribution......Page 162
 4.4 The Hypergeometric Distribution......Page 163
 4.5 The Bernoulli Distribution......Page 167
 4.6 The Binomial Distribution......Page 168
 4.7 The Multinomial Distribution......Page 172
  4.8.1 Definition and Properties of the Poisson Distribution......Page 173
  4.8.3 Poisson Distribution as a Limiting Form of the Binomial......Page 174
 4.9 The Negative Binomial Distribution......Page 179
 4.11 A Case Study......Page 182
 4.12 Review Practice Problems......Page 183
Chapter 5 Continuous Random Variables and Some Important Continuous Probability Distributions......Page 190
 5.1 Continuous Random Variables......Page 191
  5.2.1 Expected Value of Continuous Random Variables and Their Functions......Page 194
  5.2.2 The Moment‐Generating Function and Expected Value of a Special Function of X......Page 197
 5.3 Chebyshev's Inequality......Page 199
  5.4.1 Definition and Properties......Page 201
  5.4.2 Mean and Standard Deviation of the Uniform Distribution......Page 204
  5.5.1 Definition and Properties......Page 206
  5.5.2 The Standard Normal Distribution......Page 208
  5.5.3 The Moment‐Generating Function of the Normal Distribution......Page 213
 5.6 Distribution of Linear Combination of Independent Normal Variables......Page 215
  5.7.1 Approximation of the Binomial Distribution by the Normal Distribution......Page 219
 5.8 A Test of Normality......Page 222
 5.9 Probability Models Commonly used in Reliability Theory......Page 227
  5.9.1 The Lognormal Distribution......Page 228
  5.9.2 The Exponential Distribution......Page 232
  5.9.3 The Gamma Distribution......Page 237
  5.9.4 The Weibull Distribution......Page 240
 5.10 A Case Study......Page 244
 5.11 Using JMP......Page 245
 5.11 Review Practice Problems......Page 246
Chapter 6 Distribution of Functions of Random Variables......Page 254
  6.2.1 Case of Two Discrete Random Variables......Page 255
  6.2.2 Case of Two Continuous Random Variables......Page 258
  6.2.3 The Mean Value and Variance of Functions of Two Random Variables......Page 259
  6.2.4 Conditional Distributions......Page 261
  6.2.5 Correlation between Two Random Variables......Page 264
  6.2.6 Bivariate Normal Distribution......Page 267
 6.3 Extension to Several Random Variables......Page 270
 6.4 The Moment‐Generating Function Revisited......Page 271
 6.4 Review Practice Problems......Page 275
 7.1 Random Sampling......Page 279
  7.1.1 Random Sampling from an Infinite Population......Page 280
  7.1.2 Random Sampling from a Finite Population......Page 282
  7.2.2 Nonnormal Sampled Population......Page 284
  7.2.3 The Central Limit Theorem......Page 285
  7.3.1 The Chi‐Square Distribution......Page 290
  7.3.2 The Student t‐Distribution......Page 297
  7.3.3 Snedecor's F‐Distribution......Page 302
 7.4 Order Statistics......Page 305
  7.4.1 Distribution of the Largest Element in a Sample......Page 306
  7.4.2 Distribution of the Smallest Element in a Sample......Page 307
  7.4.3 Distribution of the Median of a Sample and of the kth Order Statistic......Page 308
  7.4.4 Other Uses of Order Statistics......Page 310
 7.5 Review Practice Problems......Page 312
Chapter 8 Estimation of Population Parameters......Page 315
 8.2 Point Estimators for the Population Mean and Variance......Page 316
  8.2.1 Properties of Point Estimators......Page 318
  8.2.2 Methods of Finding Point Estimators......Page 321
  8.3.1 σ2 Known......Page 327
  8.3.2 σ2 Unknown......Page 330
  8.3.3 Sample Size Is Large......Page 332
  8.4.1 Variances Are Known......Page 339
  8.4.2 Variances Are Unknown......Page 340
 8.5 Interval Estimators for the Variance of a Normal Population......Page 348
 8.6 Interval Estimator for the Ratio of Variances of Two Normal Populations......Page 353
  8.7.1 One Binomial Population......Page 357
  8.7.2 Two Binomial Populations......Page 360
 8.8 Determination of Sample Size......Page 364
  8.8.2 Difference of Two Population Means......Page 365
  8.8.3 One Population Proportion......Page 366
  8.8.4 Difference of Two Population Proportions......Page 367
 8.11 Using JMP......Page 369
 8.11 Review Practice Problems......Page 370
Chapter 9 Hypothesis Testing......Page 378
  9.2.1 Hypothesis Formulation......Page 379
  9.2.2 Risk Assessment......Page 381
  9.3.1 Case of a One‐Tail (Left‐Sided) Test......Page 384
  9.3.2 Case of a One‐Tail (Right‐Sided) Test......Page 388
  9.3.3 Case of a Two‐Tail Test......Page 389
  9.4.1 Case of a Left‐Tail Test......Page 398
  9.4.2 Case of a Right‐Tail Test......Page 399
  9.4.3 The Two‐Tail Case......Page 400
 9.5 Large Sample Theory......Page 404
  9.6.1 The Left‐Tail Test......Page 406
  9.6.2 The Right‐Tail Test......Page 407
  9.6.3 The Two‐Tail Test......Page 409
  9.7.1 Two Population Variances are Equal......Page 414
  9.7.2 Two Population Variances are Unequal......Page 418
  9.7.3 The Paired t‐Test......Page 421
  9.8.1 Test Concerning One Population Proportion......Page 427
  9.8.2 Test Concerning the Difference Between Two Population Proportions......Page 431
 9.9 Tests Concerning the Variance of a Normal Population......Page 436
 9.10 Tests Concerning the Ratio of Variances of Two Normal Populations......Page 440
 9.11 Testing of Statistical Hypotheses using Confidence Intervals......Page 444
  9.12.1 A One‐Tail Sequential Testing Procedure......Page 448
  9.12.2 A Two‐Tail Sequential Testing Procedure......Page 453
 9.13 Case Studies......Page 456
 9.14 Review Practice Problems......Page 457
Chapter 10 Elements of Reliability Theory......Page 471
  10.1.1 The Hazard Rate Function......Page 472
  10.1.2 Employing the Hazard Function......Page 481
 10.2 Estimation: Exponential Distribution......Page 483
 10.3 Hypothesis Testing: Exponential Distribution......Page 491
 10.4 Estimation: Weibull Distribution......Page 493
 10.5 Case Studies......Page 498
 10.6 Review Practice Problems......Page 500
 11.1 Introduction......Page 502
  11.2.1 Big Data......Page 503
 11.3 Data Reduction......Page 504
 11.4 Data Visualization......Page 507
  11.5.1 Missing Data......Page 516
  11.5.2 Outlier Detection and Remedial Measures......Page 517
 11.6 Classification......Page 518
  11.6.1 Evaluating a Classification Model......Page 519
 11.7 Decision Trees......Page 525
  11.7.1 Classification and Regression Trees (CART)......Page 526
 11.8 Case Studies......Page 537
 11.9 Review Practice Problems......Page 538
 12.1 Introduction......Page 544
 12.2 Similarity Measures......Page 545
  12.2.1 Common Similarity Coefficients......Page 550
 12.3 Hierarchical Clustering Methods......Page 551
  12.3.1 Single Linkage......Page 552
  12.3.2 Complete Linkage......Page 557
  12.3.3 Average Linkage......Page 560
  12.3.4 Ward's Hierarchical Clustering......Page 562
  12.4.1 K‐Means Method......Page 564
 12.5 Density‐Based Clustering......Page 570
 12.6 Model‐Based Clustering......Page 573
 12.7 A Case Study......Page 578
 12.8 Review Practice Problems......Page 579
 13.1 Introduction......Page 584
 13.2 The Chi‐Square Goodness‐of‐Fit Test......Page 585
  13.3.1 The 2×2 Case with Known Parameters......Page 594
  13.3.2 The 2×2 Case with Unknown Parameters......Page 596
  13.3.3 The r×s Contingency Table......Page 598
 13.4 Chi‐Square Test for Homogeneity......Page 603
 13.5 Comments on the Distribution of the Lack‐of‐Fit Statistics......Page 607
 13.6 Case Studies......Page 609
 13.7 Using JMP......Page 610
 13.7 Review Practice Problems......Page 611
 14.1 Introduction......Page 617
  14.2.1 One‐Sample Test......Page 618
  14.2.2 The Wilcoxon Signed‐Rank Test......Page 621
  14.2.3 Two‐Sample Test......Page 624
 14.3 Mann–Whitney (Wilcoxon) W Test for Two Samples......Page 630
  14.4.1 Runs above and below the Median......Page 634
  14.4.2 The Wald–Wolfowitz Run Test......Page 637
 14.5 Spearman Rank Correlation......Page 640
 14.6 Review Practice Problems......Page 644
Chapter 15 Simple Linear Regression Analysis......Page 648
 15.1 Introduction......Page 649
  15.2.1 Simple Linear Regression Model......Page 650
  15.2.2 Fitting a Straight Line by Least Squares......Page 653
  15.2.3 Sampling Distribution of the Estimators of Regression Coefficients......Page 657
 15.3 Unbiased Estimator of σ2......Page 663
  15.4.1 Confidence Interval for β1 with Confidence Coefficient (1−α)......Page 665
  15.4.2 Confidence Interval for β0 with Confidence Coefficient (1−α)......Page 666
  15.4.3 Confidence Interval for E(Y|X) with Confidence Coefficient (1 − α)......Page 668
  15.4.4 Prediction Interval for a Future Observation Y with Confidence Coefficient (1−α)......Page 671
  15.5.2 Test of Hypotheses for β0......Page 678
 15.6 Analysis of Variance Approach to Simple Linear Regression Analysis......Page 685
 15.7 Residual Analysis......Page 691
 15.8 Transformations......Page 700
 15.9 Inference About ρ......Page 707
 15.10 A Case Study......Page 709
 15.11 Review Practice Problems......Page 710
Chapter 16 Multiple Linear Regression Analysis......Page 719
 16.2 Multiple Linear Regression Models......Page 720
 16.3 Estimation of Regression Coefficients......Page 725
  16.3.1 Estimation of Regression Coefficients Using Matrix Notation......Page 727
  16.3.2 Properties of the Least‐Squares Estimators......Page 729
  16.3.3 The Analysis of Variance Table......Page 730
  16.3.4 More Inferences about Regression Coefficients......Page 732
  16.4.1 Single Qualitative Variable with Two Categories......Page 740
  16.4.2 Single Qualitative Variable with Three or More Categories......Page 742
 16.5 Standardized Regression Coefficients......Page 752
  16.5.1 Multicollinearity......Page 754
  16.5.2 Consequences of Multicollinearity......Page 755
  16.6.1 First Variable to Enter into the Model......Page 756
  16.7.1 Residual Analysis......Page 760
  16.7.2 Certain Criteria for Model Selection......Page 761
 16.8 Logistic Regression......Page 766
 16.9 Case Studies......Page 771
 16.10 Review Practice Problems......Page 774
Chapter 17 Analysis of Variance......Page 783
  17.2.1 Estimable Parameters......Page 784
  17.2.2 Estimable Functions......Page 786
  17.3.1 The Model and Its Analysis......Page 787
  17.3.2 Confidence Intervals for Treatment Means......Page 793
  17.3.3 Multiple Comparisons......Page 799
  17.3.4 Determination of Sample Size......Page 806
  17.3.5 The Kruskal–Wallis Test for One‐Way Layouts (Nonparametric Method)......Page 807
 17.4 Randomized Complete Block (RCB) Designs......Page 811
  17.4.1 The Friedman Fr‐Test for Randomized Complete Block Design (Nonparametric Method)......Page 818
  17.4.2 Experiments with One Missing Observation in an RCB‐Design Experiment......Page 820
  17.4.3 Experiments with Several Missing Observations in an RCB‐Design Experiment......Page 821
 17.5 Two‐Way Experimental Layouts......Page 824
  17.5.1 Two‐Way Experimental Layouts with One Observation per Cell......Page 826
  17.5.2 Two‐Way Experimental Layouts with r> 1 Observations per Cell......Page 827
  17.5.3 Blocking in Two‐Way Experimental Layouts......Page 836
  17.5.4 Extending Two‐Way Experimental Designs to n‐Way Experimental Layouts......Page 837
 17.6 Latin Square Designs......Page 839
  17.7.1 Random‐Effects Model......Page 846
  17.7.2 Mixed‐Effects Model......Page 848
  17.7.3 Nested (Hierarchical) Designs......Page 850
 17.8 A Case Study......Page 857
 17.9 Review Practice Problems......Page 858
Chapter 18 The 2k Factorial Designs......Page 873
 18.2 The Factorial Designs......Page 874
 18.3 The 2k Factorial Designs......Page 876
 18.4 Unreplicated 2k Factorial Designs......Page 885
  18.5.1 Confounding in the 2k Factorial Design......Page 893
  18.5.2 Yates's Algorithm for the 2k Factorial Designs......Page 901
  18.6.1 One‐half Replicate of a 2k Factorial Design......Page 903
  18.6.2 One‐quarter Replicate of a 2k Factorial Design......Page 908
 18.7 Case Studies......Page 913
 18.8 Review Practice Problems......Page 915
 19.1 Introduction......Page 923
  19.1.1 Basic Concepts of Response Surface Methodology......Page 924
 19.2 First‐Order Designs......Page 929
 19.3 Second‐Order Designs......Page 943
  19.3.1 Central Composite Designs (CCDs)......Page 944
  19.3.2 Some Other First‐Order and Second‐Order Designs......Page 954
 19.4 Determination of Optimum or Near‐Optimum Point......Page 962
  19.4.1 The Method of Steepest Ascent......Page 963
  19.4.2 Analysis of a Fitted Second‐Order Response Surface......Page 967
 19.5 Anova Table for a Second‐Order Model......Page 972
 19.6 Case Studies......Page 974
 19.7 Review Practice Problems......Page 976
Chapter 20 Statistical Quality Control—Phase I Control Charts......Page 984
Chapter 21 Statistical Quality Control—Phase II Control Charts......Page 986
Appendix A Statistical Tables......Page 988
Appendix B Answers to Selected Problems......Page 995
Appendix C Bibliography......Page 1018
Index......Page 1029
EULA......Page 1043