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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 | |