ISBN-13: 9781119516637 / Angielski / Twarda / 2020 / 1040 str.
ISBN-13: 9781119516637 / Angielski / Twarda / 2020 / 1040 str.
Preface xviiAcknowledgments xxiAbout The Companion Site xxiii1 Introduction 11.1 Designed Experiment 21.1.1 Motivation for the Study 21.1.2 Investigation 31.1.3 Changing Criteria 31.1.4 A Summary of the Various Phases of the Investigation 51.2 A Survey 61.3 An Observational Study 61.4 A Set of Historical Data 71.5 A Brief Description of What is Covered in this Book 7Part I Fundamentals of Probability and Statistics2 Describing Data Graphically and Numerically 132.1 Getting Started with Statistics 142.1.1 What is Statistics? 142.1.2 Population and Sample in a Statistical Study 142.2 Classification of Various Types of Data 182.2.1 Nominal Data 182.2.2 Ordinal Data 192.2.3 Interval Data 192.2.4 Ratio Data 192.3 Frequency Distribution Tables for Qualitative and Quantitative Data 202.3.1 Qualitative Data 212.3.2 Quantitative Data 242.4 Graphical Description of Qualitative and Quantitative Data 302.4.1 Dot Plot 302.4.2 Pie Chart 312.4.3 Bar Chart 332.4.4 Histograms 372.4.5 Line Graph 442.4.6 Stem-and-Leaf Plot 452.5 Numerical Measures of Quantitative Data 502.5.1 Measures of Centrality 512.5.2 Measures of Dispersion 562.6 Numerical Measures of Grouped Data 672.6.1 Mean of a Grouped Data 672.6.2 Median of a Grouped Data 682.6.3 Mode of a Grouped Data 692.6.4 Variance of a Grouped Data 692.7 Measures of Relative Position 702.7.1 Percentiles 712.7.2 Quartiles 722.7.3 Interquartile Range (IQR) 722.7.4 Coefficient of Variation 732.8 Box-Whisker Plot 752.8.1 Construction of a Box Plot 752.8.2 How to Use the Box Plot 762.9 Measures of Association 802.10 Case Studies 842.10.1 About St. Luke's Hospital 852.11 Using JMP 86Review Practice Problems 873 Elements of Probability 973.1 Introduction 973.2 Random Experiments, Sample Spaces, and Events 983.2.1 Random Experiments and Sample Spaces 983.2.2 Events 993.3 Concepts of Probability 1033.4 Techniques of Counting Sample Points 1083.4.1 Tree Diagram 1083.4.2 Permutations 1103.4.3 Combinations 1103.4.4 Arrangements of n Objects Involving Several Kinds of Objects 1113.5 Conditional Probability 1133.6 Bayes's Theorem 1163.7 Introducing Random Variables 120Review Practice Problems 1224 Discrete Random Variables and Some Important Discrete Probability Distributions 1284.1 Graphical Descriptions of Discrete Distributions 1294.2 Mean and Variance of a Discrete Random Variable 1304.2.1 Expected Value of Discrete Random Variables and Their Functions 1304.2.2 The Moment-Generating Function-Expected Value of a Special Function of X 1334.3 The Discrete Uniform Distribution 1364.4 The Hypergeometric Distribution 1374.5 The Bernoulli Distribution 1414.6 The Binomial Distribution 1424.7 The Multinomial Distribution 1464.8 The Poisson Distribution 1474.8.1 Definition and Properties of the Poisson Distribution 1474.8.2 Poisson Process 1484.8.3 Poisson Distribution as a Limiting Form of the Binomial 1484.9 The Negative Binomial Distribution 1534.10 Some Derivations and Proofs (Optional) 1564.11 A Case Study 1564.12 Using JMP 157Review Practice Problems 1575 Continuous Random Variables and Some Important Continuous Probability Distributions 1645.1 Continuous Random Variables 1655.2 Mean and Variance of Continuous Random Variables 1685.2.1 Expected Value of Continuous Random Variables and Their Functions 1685.2.2 The Moment-Generating Function and Expected Value of a Special Function of X 1715.3 Chebyshev's Inequality 1735.4 The Uniform Distribution 1755.4.1 Definition and Properties 1755.4.2 Mean and Standard Deviation of the Uniform Distribution 1785.5 The Normal Distribution 1805.5.1 Definition and Properties 1805.5.2 The Standard Normal Distribution 1825.5.3 The Moment-Generating Function of the Normal Distribution 1875.6 Distribution of Linear Combination of Independent Normal Variables 1895.7 Approximation of the Binomial and Poisson Distributions by the Normal Distribution 1935.7.1 Approximation of the Binomial Distribution by the Normal Distribution 1935.7.2 Approximation of the Poisson Distribution by the Normal Distribution 1965.8 A Test of Normality 1965.9 Probability Models Commonly used in Reliability Theory 2015.9.1 The Lognormal Distribution 2025.9.2 The Exponential Distribution 2065.9.3 The Gamma Distribution 2115.9.4 The Weibull Distribution 2145.10 A Case Study 2185.11 Using JMP 219Review Practice Problems 2206 Distribution of Functions Of Random Variables 2286.1 Introduction 2296.2 Distribution Functions of Two Random Variables 2296.2.1 Case of Two Discrete Random Variables 2296.2.2 Case of Two Continuous Random Variables 2326.2.3 The Mean Value and Variance of Functions of Two Random Variables 2336.2.4 Conditional Distributions 2356.2.5 Correlation between Two Random Variables 2386.2.6 Bivariate Normal Distribution 2416.3 Extension to Several Random Variables 2446.4 The Moment-Generating Function Revisited 245Review Practice Problems 2497 Sampling Distributions 2537.1 Random Sampling 2537.1.1 Random Sampling from an Infinite Population 2547.1.2 Random Sampling from a Finite Population 2567.2 The Sampling Distribution of the Sample Mean 2587.2.1 Normal Sampled Population 2587.2.2 Nonnormal Sampled Population 2587.2.3 The Central Limit Theorem 2597.3 Sampling from a Normal Population 2647.3.1 The Chi-Square Distribution 2647.3.2 The Student t-Distribution 2717.3.3 Snedecor's F-Distribution 2767.4 Order Statistics 2797.4.1 Distribution of the Largest Element in a Sample 2807.4.2 Distribution of the Smallest Element in a Sample 2817.4.3 Distribution of the Median of a Sample and of the kth Order Statistic 2827.4.4 Other Uses of Order Statistics 2847.5 Using JMP 286Review Practice Problems 2868 Estimation of Population Parameters 2898.1 Introduction 2908.2 Point Estimators for the Population Mean and Variance 2908.2.1 Properties of Point Estimators 2928.2.2 Methods of Finding Point Estimators 2958.3 Interval Estimators for the Mean mu of a Normal Population 3018.3.1 sigma² Known 3018.3.2 sigma² Unknown 3048.3.3 Sample Size is Large 3068.4 Interval Estimators for The Difference of Means of Two Normal Populations 3138.4.1 Variances are Known 3138.4.2 Variances are Unknown 3148.5 Interval Estimators for the Variance of a Normal Population 3228.6 Interval Estimator for the Ratio of Variances of Two Normal Populations 3278.7 Point and Interval Estimators for the Parameters of Binomial Populations 3318.7.1 One Binomial Population 3318.7.2 Two Binomial Populations 3348.8 Determination of Sample Size 3388.8.1 One Population Mean 3398.8.2 Difference of Two Population Means 3398.8.3 One Population Proportion 3408.8.4 Difference of Two Population Proportions 3418.9 Some Supplemental Information 3438.10 A Case Study 3438.11 Using JMP 343Review Practice Problems 3449 Hypothesis Testing 3529.1 Introduction 3539.2 Basic Concepts of Testing a Statistical Hypothesis 3539.2.1 Hypothesis Formulation 3539.2.2 Risk Assessment 3559.3 Tests Concerning the Mean of a Normal Population Having Known Variance 3589.3.1 Case of a One-Tail (Left-Sided) Test 3589.3.2 Case of a One-Tail (Right-Sided) Test 3629.3.3 Case of a Two-Tail Test 3639.4 Tests Concerning the Mean of a Normal Population Having Unknown Variance 3729.4.1 Case of a Left-Tail Test 3729.4.2 Case of a Right-Tail Test 3739.4.3 The Two-Tail Case 3749.5 Large Sample Theory 3789.6 Tests Concerning the Difference of Means of Two Populations Having Distributions with Known Variances 3809.6.1 The Left-Tail Test 3809.6.2 The Right-Tail Test 3819.6.3 The Two-Tail Test 3839.7 Tests Concerning the Difference of Means of Two Populations Having Normal Distributions with Unknown Variances 3889.7.1 Two Population Variances are Equal 3889.7.2 Two Population Variances are Unequal 3929.7.3 The Paired t-Test 3959.8 Testing Population Proportions 4019.8.1 Test Concerning One Population Proportion 4019.8.2 Test Concerning the Difference Between Two Population Proportions 4059.9 Tests Concerning the Variance of a Normal Population 4109.10 Tests Concerning the Ratio of Variances of Two Normal Populations 4149.11 Testing of Statistical Hypotheses using Confidence Intervals 4189.12 Sequential Tests of Hypotheses 4229.12.1 A One-Tail Sequential Testing Procedure 4229.12.2 A Two-Tail Sequential Testing Procedure 4279.13 Case Studies 4309.14 Using JMP 431Review Practice Problems 431Part II Statistics in Actions10 Elements of Reliability Theory 44510.1 The Reliability Function 44610.1.1 The Hazard Rate Function 44610.1.2 Employing the Hazard Function 45510.2 Estimation: Exponential Distribution 45710.3 Hypothesis Testing: Exponential Distribution 46510.4 Estimation: Weibull Distribution 46710.5 Case Studies 47210.6 Using JMP 474Review Practice Problems 47411 On Data Mining 47611.1 Introduction 47611.2 What is Data Mining? 47711.2.1 Big Data 47711.3 Data Reduction 47811.4 Data Visualization 48111.5 Data Preparation 49011.5.1 Missing Data 49011.5.2 Outlier Detection and Remedial Measures 49111.6 Classification 49211.6.1 Evaluating a Classification Model 49311.7 Decision Trees 49911.7.1 Classification and Regression Trees (CART) 50011.7.2 Further Reading 51111.8 Case Studies 51111.9 Using JMP 512Review Practice Problems 51212 Cluster Analysis 51812.1 Introduction 51812.2 Similarity Measures 51912.2.1 Common Similarity Coefficients 52412.3 Hierarchical Clustering Methods 52512.3.1 Single Linkage 52612.3.2 Complete Linkage 53112.3.3 Average Linkage 53412.3.4 Ward's Hierarchical Clustering 53612.4 Nonhierarchical Clustering Methods 53812.4.1 K-Means Method 53812.5 Density-Based Clustering 54412.6 Model-Based Clustering 54712.7 A Case Study 55212.8 Using JMP 553Review Practice Problems 55313 Analysis of Categorical Data 55813.1 Introduction 55813.2 The Chi-Square Goodness-of-Fit Test 55913.3 Contingency Tables 56813.3.1 The 2 × 2 Case with Known Parameters 56813.3.2 The 2 × 2 Case with Unknown Parameters 57013.3.3 The r × s Contingency Table 57213.4 Chi-Square Test for Homogeneity 57713.5 Comments on the Distribution of the Lack-of-Fit Statistics 58113.6 Case Studies 58313.7 Using JMP 584Review Practice Problems 58514 Nonparametric Tests 59114.1 Introduction 59114.2 The Sign Test 59214.2.1 One-Sample Test 59214.2.2 The Wilcoxon Signed-Rank Test 59514.2.3 Two-Sample Test 59814.3 Mann-Whitney (Wilcoxon) W Test for Two Samples 60414.4 Runs Test 60814.4.1 Runs above and below the Median 60814.4.2 The Wald-Wolfowitz Run Test 61114.5 Spearman Rank Correlation 61414.6 Using JMP 618Review Practice Problems 61815 Simple Linear Regression Analysis 62215.1 Introduction 62315.2 Fitting the Simple Linear Regression Model 62415.2.1 Simple Linear Regression Model 62415.2.2 Fitting a Straight Line by Least Squares 62715.2.3 Sampling Distribution of the Estimators of Regression Coefficients 63115.3 Unbiased Estimator of sigma² 63715.4 Further Inferences Concerning Regression Coefficients (ß0, ß1), E(Y ), and Y 63915.4.1 Confidence Interval for ß1 with Confidence Coefficient (1 . alpha) 63915.4.2 Confidence Interval for ß0 with Confidence Coefficient (1 . alpha) 64015.4.3 Confidence Interval for E(Y |X) with Confidence Coefficient (1 . alpha) 64215.4.4 Prediction Interval for a Future Observation Y with Confidence Coefficient (1 . alpha) 64515.5 Tests of Hypotheses for ß0 and ß1 65215.5.1 Test of Hypotheses for ß1 65215.5.2 Test of Hypotheses for ß0 65215.6 Analysis of Variance Approach to Simple Linear Regression Analysis 65915.7 Residual Analysis 66515.8 Transformations 67415.9 Inference About rho 68115.10A Case Study 68315.11 Using JMP 684Review Practice Problems 68416 Multiple Linear Regression Analysis 69316.1 Introduction 69416.2 Multiple Linear Regression Models 69416.3 Estimation of Regression Coefficients 69916.3.1 Estimation of Regression Coefficients Using Matrix Notation 70116.3.2 Properties of the Least-Squares Estimators 70316.3.3 The Analysis of Variance Table 70416.3.4 More Inferences about Regression Coefficients 70616.4 Multiple Linear Regression Model Using Quantitative and Qualitative Predictor Variables 71416.4.1 Single Qualitative Variable with Two Categories 71416.4.2 Single Qualitative Variable with Three or More Categories 71616.5 Standardized Regression Coefficients 72616.5.1 Multicollinearity 72816.5.2 Consequences of Multicollinearity 72916.6 Building Regression Type Prediction Models 73016.6.1 First Variable to Enter into the Model 73016.7 Residual Analysis and Certain Criteria for Model Selection 73416.7.1 Residual Analysis 73416.7.2 Certain Criteria for Model Selection 73516.8 Logistic Regression 74016.9 Case Studies 74516.10 Using JMP 748Review Practice Problems 74817 Analysis of Variance 75717.1 Introduction 75817.2 The Design Models 75817.2.1 Estimable Parameters 75817.2.2 Estimable Functions 76017.3 One-Way Experimental Layouts 76117.3.1 The Model and Its Analysis 76117.3.2 Confidence Intervals for Treatment Means 76717.3.3 Multiple Comparisons 77317.3.4 Determination of Sample Size 78017.3.5 The Kruskal-Wallis Test for One-Way Layouts (Nonparametric Method) 78117.4 Randomized Complete Block (RCB) Designs 78517.4.1 The Friedman Fr-Test for Randomized Complete Block Design (Nonparametric Method) 79217.4.2 Experiments with One Missing Observation in an RCB-Design Experiment 79417.4.3 Experiments with Several Missing Observations in an RCB-Design Experiment 79517.5 Two-Way Experimental Layouts 79817.5.1 Two-Way Experimental Layouts with One Observation per Cell 80017.5.2 Two-Way Experimental Layouts with r > 1 Observations per Cell 80117.5.3 Blocking in Two-Way Experimental Layouts 81017.5.4 Extending Two-Way Experimental Designs to n-Way Experimental Layouts 81117.6 Latin Square Designs 81317.7 Random-Effects and Mixed-Effects Models 82017.7.1 Random-Effects Model 82017.7.2 Mixed-Effects Model 82217.7.3 Nested (Hierarchical) Designs 82417.8 A Case Study 83117.9 Using JMP 832Review Practice Problems 83218 The 2^k Factorial Designs 84718.1 Introduction 84818.2 The Factorial Designs 84818.3 The 2^k Factorial Designs 85018.4 Unreplicated 2^k Factorial Designs 85918.5 Blocking in the 2^k Factorial Design 86718.5.1 Confounding in the 2^k Factorial Design 86718.5.2 Yates's Algorithm for the 2^k Factorial Designs 87518.6 The 2k Fractional Factorial Designs 87718.6.1 One-half Replicate of a 2^k Factorial Design 87718.6.2 One-quarter Replicate of a 2^k Factorial Design 88218.7 Case Studies 88718.8 Using JMP 889Review Practice Problems 88919 Response Surfaces 89719.1 Introduction 89719.1.1 Basic Concepts of Response Surface Methodology 89819.2 First-Order Designs 90319.3 Second-Order Designs 91719.3.1 Central Composite Designs (CCDs) 91819.3.2 Some Other First-Order and Second-Order Designs 92819.4 Determination of Optimum or Near-Optimum Point 93619.4.1 The Method of Steepest Ascent 93719.4.2 Analysis of a Fitted Second-Order Response Surface 94119.5 Anova Table for a Second-Order Model 94619.6 Case Studies 94819.7 Using JMP 950Review Practice Problems 95020 Statistical Quality Control--Phase I Control Charts 95821 Statistical Quality Control--Phase II Control Charts 960Appendices 961Appendix A Statistical Tables 962Appendix B Answers to Selected Problems 969Appendix C Bibliography 992Index 1003
BHISHAM C. GUPTA, PHD, is Professor Emeritus of Statistics in the Department of Mathematics and Statistics at the University of Southern Maine, and the co-author of Statistics and Probability with Applications for Engineers and Scientists.IRWIN GUTTMAN, PHD, is Professor Emeritus of Statistics in the Department of Mathematics at the State University of New York at Buffalo and Department of Statistics at the University of Toronto, Canada. He is the co-author of Statistics and Probability with Applications for Engineers and Scientists.KALANKA P. JAYALATH, PHD, is Assistant Professor in the Department of Mathematics and Statistics at the University of Houston.
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