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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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Discrete Probability Functions | |

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Continuous Probability Functions | |

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Conditional Probability | |

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Independence | |

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Repeated Independent Trials | |

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Combinatorics | |

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Combinatorial Probability | |

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Random Variables | |

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The Probability Density Function | |

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The Hypergeometric and Binomial Distributions | |

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The Cumulative Distribution Function | |

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Joint Densities | |

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Independent Random Variables | |

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Combining and Transforming Random Variables | |

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Order Statistics | |

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Conditional Densities | |

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Expected Values | |

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Properties of Expected Values | |

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The Variance | |

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Properties of Variances | |

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Chebyshev's Inequality | |

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Higher Moments | |

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Moment-Generating Functions | |

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Minitab Applications | |

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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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Minitab Applications | |

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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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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 | |

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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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Point Estimates for ï¿½Ç m and ï¿½Ç s2 | |

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The ï¿½Ç c2 Distribution | |

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Inferences about ï¿½Ç s2 | |

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The F and t Distributions | |

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Drawing Inferences about ï¿½Ç m | |

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Minitab Applications | |

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Some Distribution Results for Y and S | |

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Appendix 7.A.3: A Proof of Theorem 7.3.5 | |

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A Proof That the One-Sample t | |

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Test Is a GLRT | |

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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: = The Two-Sample t Test | |

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Testing H 0: = 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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A Derivation of the Two-Sample t | |

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Test (A Proof of Theorem 9.2.2.) | |

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Power Calculations for a Two-Sample t Test | |

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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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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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Minitab Applications | |

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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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Minitab Applications | |

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A Proof of Theorem 12.2.2 | |

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The Distribution of $E{ down 12 SSTR/ up 12 (k-1)} over { down 12 SSE/ up 12 (n-k)} | |

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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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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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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 | |