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Introduction | |
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A Brief History | |
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Some Examples | |
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A Chapter Summary | |
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Probability | |
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Sample Spaces and the Algebra of Sets | |
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The Probability Function | |
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Conditional Probability | |
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Independence | |
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Combinatorics | |
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Combinatorial Probability | |
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Random Variables | |
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Binomial and Hypergeometric Probabilities | |
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Discrete Random Variables | |
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Continuous Random Variables | |
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Expected Values | |
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The Variance | |
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Joint Densities | |
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Combining Random Variables | |
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Further Properties of the Mean and Variance | |
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Order Statistics | |
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Conditional Densities | |
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Moment Generating Functions | |
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Odds and Ends | |
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Special Distributions | |
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The Poisson Distribution | |
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The Normal Distribution | |
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The Geometric Distribution | |
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The Negative Binomial Distribution | |
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The Gamma Distribution | |
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Appendix 4.A.1: MINITAB Applications | |
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Appendix 4.A.2: A Proof of the Central Limit Theorem | |
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Estimation | |
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Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments | |
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Interval Estimation | |
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Properties of Estimators | |
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Minimum-Variance Estimators: The Cramer-Rao Lower Bound | |
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Sufficiency | |
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Consistency | |
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Appendix 5.A.1: MINITAB Applications | |
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Hypothesis Testing | |
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The Decision Rule | |
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Testing Binomial Data H0: p = p 0 | |
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Type I and Type II Errors | |
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A Notion of Optimality: The Generalized Likelihood Ratio | |
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The Normal Distribution | |
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Comparing and . Deriving the distribution of . Drawing inferences about m | |
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Drawing inferences about . Odds and Ends | |
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Types of Data: A Brief Overview | |
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Classifying Data | |
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Two-Sample Problems | |
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Testing H 0: mx = mY The Two-Sample t Test | |
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Testing H0: s2x = s2Y The F Test | |
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Binomial Data: Testing H 0: px = py | |
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Confidence Intervals for the Two-Sample Problem | |
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Appendix 9.A.1: A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2.) | |
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Appendix 9.A.2: Power Calculations for a Two-Sample t Test | |
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Appendix 9.A.3: MINITAB Applications | |
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Goodness-of-Fit Tests | |
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The Multinomial Distribution | |
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Goodness-of-Fit Tests: All Parameters Known | |
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Goodness-of-Fit Tests: Parameters Unknown | |
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Contingency Tables | |
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Appendix 10.A.1: MINITAB Applications | |
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Regression | |
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The Method of Least Squares | |
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The Linear Model | |
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Covariance and Correlation | |
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The Bivariate Normal Distribution | |
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Appendix 11.A.1: MINITAB Applications | |
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Appendix 11.A.2: A Proof of Theorem 11.3.3 | |
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The Analysis of Variance | |
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The F Test | |
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Multiple Comparisons: Tukey's Method | |
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Testing Subhypotheses with Orthogonal Contrasts | |
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Data Transformations | |
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Appendix 12.A.1: MINITAB Applications | |
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Appendix 12.A.2: A Proof of Theorem 12.2.2 | |
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Appendix 12.A.3: The Distribution of When H1 Is True | |
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Randomized Block Designs | |
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The F Test for a Randomized Block Design | |
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The Paired t Test | |
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Appendix 13.A.1: MINITAB Applications | |
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Nonparametric Statistics | |
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The Sign Test | |
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The Wilcoxon Signed Rank Test | |
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The Kruskal-Wallis Test | |
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The Friedman Test | |
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Appendix 14.A.1: MINITAB Applications | |
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Appendix: Statistical Tables | |
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Answers to Selected Odd-Numbered Questions | |
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Bibliography | |
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Index | |