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Preface | |

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Introduction to Statistics | |

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Introduction | |

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Data Collection and Descriptive Statistics | |

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Inferential Statistics and Probability Models | |

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Populations and Samples | |

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A Brief History of Statistics | |

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Problems | |

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Descriptive Statistics | |

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Introduction | |

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Describing Data Sets | |

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Frequency Tables and Graphs | |

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Relative Frequency Tables and Graphs | |

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Grouped Data, Histograms, Ogives, and Stem and Leaf Plots | |

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Summarizing Data Sets | |

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Sample Mean, Sample Median, and Sample Mode | |

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Sample Variance and Sample Standard Deviation | |

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Sample Percentiles and Box Plots | |

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Chebyshev's Inequality | |

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Normal Data Sets | |

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Paired Data Sets and the Sample Correlation Coefficient | |

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Problems | |

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Elements of Probability | |

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Introduction | |

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Sample Space and Events | |

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Venn Diagrams and the Algebra of Events | |

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Axioms of Probability | |

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Sample Spaces Having Equally Likely Outcomes | |

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Conditional Probability | |

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Bayes' Formula | |

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Independent Events | |

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Problems | |

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Random Variables and Expectation | |

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Random Variables | |

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Types of Random Variables | |

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Jointly Distributed Random Variables | |

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Independent Random Variables | |

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Conditional Distributions | |

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Expectation | |

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Properties of the Expected Value | |

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Expected Value of Sums of Random Variables | |

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Variance | |

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Covariance and Variance of Sums of Random Variables | |

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Moment Generating Functions | |

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Chebyshev's Inequality and the Weak Law of Large Numbers | |

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Problems | |

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Special Random Variables | |

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The Bernoulli and Binomial Random Variables | |

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Computing the Binomial Distribution Function | |

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The Poisson Random Variable | |

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Computing the Poisson Distribution Function | |

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The Hypergeometric Random Variable | |

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The Uniform Random Variable | |

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Normal Random Variables | |

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Exponential Random Variables | |

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The Poisson Process | |

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The Gamma Distribution | |

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Distributions Arising from the Normal | |

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The Chi-Square Distribution | |

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The Relation Between Chi-Square and Gamma Random Variables | |

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The t-Distribution | |

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The F-Distribution | |

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The Logistics Distribution | |

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Problems | |

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Distributions of Sampling Statistics | |

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Introduction | |

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The Sample Mean | |

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The Central Limit Theorem | |

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Approximate Distribution of the Sample Mean | |

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How Large a Sample is Needed? | |

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The Sample Variance | |

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Sampling Distributions from a Normal Population | |

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Distribution of the Sample Mean | |

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Joint Distribution of X and S[superscript 2] | |

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Sampling from a Finite Population | |

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Problems | |

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Parameter Estimation | |

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Introduction | |

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Maximum Likelihood Estimators | |

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Estimating Life Distributions | |

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Interval Estimates | |

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Confidence Interval for a Normal Mean When the Variance is Unknown | |

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Confidence Intervals for the Variances of a Normal Distribution | |

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Estimating the Difference in Means of Two Normal Populations | |

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Approximate Confidence Interval for the Mean of a Bernoulli Random Variable | |

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Confidence Interval of the Mean of the Exponential Distribution | |

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Evaluating a Point Estimator | |

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The Bayes Estimator | |

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Problems | |

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Hypothesis Testing | |

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Introduction | |

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Significance Levels | |

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Tests Concerning the Mean of a Normal Population | |

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Case of Known Variance | |

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Case of Unknown Variance: The t-Test | |

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Testing the Equality of Means of Two Normal Populations | |

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Case of Known Variances | |

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Case of Unknown Variances | |

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Case of Unknown and Unequal Variances | |

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The Paired t-Test | |

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Hypothesis Tests Concerning the Variance of a Normal Population | |

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Testing for the Equality of Variances of Two Normal Populations | |

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Hypothesis Tests in Bernoulli Populations | |

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Testing the Equality of Parameters in Two Bernoulli Populations | |

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Tests Concerning the Mean of a Poisson Distribution | |

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Testing the Relationship Between Two Poisson Parameters | |

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Problems | |

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Regression | |

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Introduction | |

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Least Squares Estimators of the Regression Parameters | |

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Distribution of the Estimators | |

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Statistical Inferences about the Regression Parameters | |

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Inferences Concerning [beta] | |

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Regression to the Mean | |

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Inferences Concerning [alpha] | |

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Inferences Concerning the Mean Response [alpha] + [beta]x[subscript 0] | |

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Prediction Interval of a Future Response | |

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Summary of Distributional Results | |

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The Coefficient of Determination and the Sample Correlation Coefficient | |

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Analysis of Residuals: Assessing the Model | |

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Transforming to Linearity | |

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Weighted Least Squares | |

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Polynomial Regression | |

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Multiple Linear Regression | |

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Predicting Future Responses | |

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Logistic Regression Models for Binary Output Data | |

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Problems | |

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Analysis of Variance | |

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Introduction | |

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An Overview | |

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One-Way Analysis of Variance | |

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Multiple Comparisons of Sample Means | |

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One-Way Analysis of Variance with Unequal Sample Sizes | |

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Two-Factor Analysis of Variance: Introduction and Parameter Estimation | |

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Two-Factor Analysis of Variance: Testing Hypotheses | |

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Two-Way Analysis of Variance with Interaction | |

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Problems | |

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Goodness of Fit Tests and Categorical Data Analysis | |

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Introduction | |

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Goodness of Fit Tests When all Parameters are Specified | |

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Determining the Critical Region by Simulation | |

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Goodness of Fit Tests When Some Parameters are Unspecified | |

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Tests of Independence in Contingency Tables | |

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Tests of Independence in Contingency Tables Having Fixed Marginal Totals | |

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The Kolmogorov-Smirnov Goodness of Fit Test for Continuous Data | |

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Problems | |

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Nonparametric Hypothesis Tests | |

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Introduction | |

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The Sign Test | |

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The Signed Rank Test | |

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The Two-Sample Problem | |

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The Classical Approximation and Simulation | |

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The Runs Test for Randomness | |

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Problems | |

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Quality Control | |

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Introduction | |

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Control Charts for Average Values: The X-Control Chart | |

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Case of Unknown [mu] and [sigma] | |

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S-Control Charts | |

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Control Charts for the Fraction Defective | |

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Control Charts for Number of Defects | |

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Other Control Charts for Detecting Changes in the Population Mean | |

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Moving-Average Control Charts | |

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Exponentially Weighted Moving-Average Control Charts | |

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Cumulative Sum Control Charts | |

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Problems | |

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Life Testing | |

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Introduction | |

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Hazard Rate Functions | |

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The Exponential Distribution in Life Testing | |

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Simultaneous Testing--Stopping at the rth Failure | |

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Sequential Testing | |

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Simultaneous Testing--Stopping by a Fixed Time | |

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The Bayesian Approach | |

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A Two-Sample Problem | |

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The Weibull Distribution in Life Testing | |

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Parameter Estimation by Least Squares | |

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Problems | |

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Appendix of Tables | |

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Index | |