Chapter 1 Introduction to Probability and Counting

1.1 Interpreting Probabilities

1.2 Sample Spaces and Events

Mutually Exclusive Events

1.3 Permutations and Combinations

Counting Permutations

Counting Combinations

Permutations of Indistinguishable Objects

Chapter Summary

Exercises

Review Exercises

Chapter 2 Some Probability Laws

2.1 Axioms of Probability

The General Addition Rule

2.2 Conditional Probability

2.3 Independence of the Multiplication Rule

The Multiplication Rule

2.4 Bayes' Theorem

Chapter Summary

Exercises

Review Exercises

Chapter 3 Discrete Distributions

3.1 Random Variables

3.2 Discrete Probability Densities

Cumulative Distribution

3.3 Expectation and Distribution Parameters

Variance and Standard Deviation

3.4 Geometric Distribution and the Moment Generating Function

Geometric Distribution

Moment Generating Function

3.5 Binomial Distribution

3.6 Negative Binomial Distribution

3.7 Hypergeometric Distribution

3.8 Poisson Distribution

3.9 Simulating a Discrete Distribution

Chapter Summary

Exercises

Review Exercises

Chapter 4 Continuous Distributions

4.1 Continuous Densities

Cumulative Distribution

Uniform Distribution

4.2 Expectation and Distribution Parameters

4.3 Gamma, Exponential, and Chi-Squared Distributions

Gamma Distribution

Exponential Distribution

Chi-Squared Distribution

4.4 Normal Distribution

Standard Normal Distribution

4.5 Normal Probability Rule and Chebyshev's Inequality

4.6 Normal Approximation to the Binomial Distribution

4.7 Weibull Distribution and Reliability

Reliability

Reliability of Series and Parallel Systems

4.8 Transformation of Variables

4.9 Simulating a Continuous Distribution

Chapter Summary

Exercises

Review Exercises

Chapter 5 Joint Distributions

5.1 Joint Densities and Independence

Marginal Distributions: Discrete

Joint and Marginal Distributions: Continuous

Independence

5.2 Expectation and Covariance

Covariance

5.3 Correlation

5.4 Conditional Densities and Regression

Curves of Regression

5.5 Transformation of Variables

Chapter Summary

Exercises

Review Exercises

Chapter 6 Descriptive Statistics

6.1 Random Sampling

6.2 Picturing the Distribution

Stem-and-Leaf Diagram

Histograms and Ogives

Cumulative Distribution Plots (Ogives)

6.3 Sample Statistics

Location Statistics

Measures of Variability

6.4 Boxplots

Chapter Summary

Exercises

Review Exercises

Chapter 7 Estimation

7.1 Point Estimation

7.2 The Method of Moments and Maximum Likelihood

Maximum Likelihood Estimators

7.3 Functions of Random Variables--Distribution of X

Distribution of X

7.4 Interval Estimation and the Central Limit Theorem

Confidence Interval on the Mean: Variance Known

Central Limit Theorem

Chapter Summary

Exercises

Review Exercises

Chapter 8 Inferences on the Mean and Variance of a Distribution

8.1 Interval Estimation of Variability

8.2 Estimating the Mean and the Student-t Distribution

The T Distribution

Confidence Interval on the Mean: Variance Estimated

8.3 Hypothesis Testing

8.4 Significance Testing

8.5 Hypothesis and Significance Tests on the Mean

8.6 Hypothesis Tests on the Variance

8.7 Alternative Nonparametric Methods

Sign Test for Median

Wilcoxon Signed-Rank Test

Chapter Summary

Exercises

Review Exercises

Chapter 9 Inferences on Proportions

9.1 Estimating Proportions

Confidence Interval on p

Sample Size for Estimating p

9.2 Testing Hypotheses on a Proportion

9.3 Comparing Two Proportions: Estimation

Confidence Interval on p1 - p2

9.4 Comparing Two Proportions: Hypothesis Testing

Pooled Proportions

Chapter Summary

Exercises

Review Exercises

Chapter 10 Comparing Two Means and Two Variances

10.1 Point Estimation: Independent Samples

10.2 Comparing Variances: The F Distribution

10.3 Comparing Means: Variances Equal (Pooled Test)

Confidence Interval on u1 --u2: Pooled

Pooled T Test

10.4 Comparing Means: Variances Unequal

10.5 Comparing Means: Paired Data

Paired T Test

10.6 Alternative Nonparametric Methods

Wilcoxon Rank-Sum Test

Wilcoxon Signed-Rank Test for Paired Observations

10.7 A Note on Technology

Chapter Summary

Exercises

Review Exercises

Chapter 11 Simple Linear Regression and Correlation

11.1 Model and Parameter Estimation

Description of the Model

Least-Squares Estimation

11.2 Properties of Least-Squares Estimators

Distribution of B1

Distribution of B0

Estimator of a2

Summary of Theoretical Results

11.3 Confidence Interval Estimation and Hypothesis Testing

Inferences about Slope

Inferences about Intercept

Inferences about Estimated Mean

Inferences about Single Predicted Value

11.4 Repeated Measures and Lack of Fit

11.5 Residual Analysis

Residual Plots

Checking for Normality: Stem-and-Leaf Plots and Boxplots

11.6 Correlation

Interval Estimation and Hypothesis Tests on p

Coefficient of Determination

Chapter Summary

Exercises

Review Exercises

Chapter 12 Multiple Linear Regression Models

12.1 Least-Squares Procedures for Model Fitting

Polynomial Model of Degree p AAA Multiple Linear Regression Model

12.2 A Matrix Approach to Least Squares

The Normal Equations

Solving the Normal Equations

Simple Linear Regression: Matrix Formulation

Polynomial Model: Matrix Formulation

12.3 Properties of the Least-Squares Estimators

Expected Value of B

Estimation of a2 and Variance of B

12.4 Interval Estimation

Confidence Interval on Coefficients

Confidence Interval on Estimated Mean

Prediction Interval on a Single Predicted Response

12.5 Testing Hypotheses about Model Parameters

Testing a Single Predictor Variable

Testing for Significant Regression

Testing a Subset of Predictor Variables

12.6 Use of Indicator or "Dummy" Variables

12.7 Criteria for Variable Selection

Forward Selection Method

Backward Elimination Procedure

Stepwise Method

Maximum R2 Method

Mallows Ck Statistic

PRESS Statistic

12.8 Model Transformation and Concluding Remarks

Chapter Summary

Exercises

Review Exercises

Chapter 13 Analysis of Variance

13.1 One-Way Classification Fixed-Effects Model

The Model

Testing H0

13.2 Comparing Variances

13.3 Pairwise Comparisons

Bonferroni T Tests

Duncan's Multiple Range Test

Tukey's Test

13.4 Testing Contrasts

13.5 Randomized Complete Block Design

The Model

Testing H0

Effectiveness of Blocking

Paired Comparisons

13.6 Latin Squares

13.7 Random-Effects Models

One-Way Classification

13.8 Design Models in Matrix Form

13.9 Alternative Nonparametric Methods

Kruskal-Wallis Test

Friedman Test

Chapter Summary

Exercises

Review Exercises

Chapter 14 Factorial Experiments

14.1 Two-Factor Analysis of Variance

Testing H0

Paired Comparisons

Sample Size

14.2 Extension to Three Factors

14.3 Random and Mixed Model Factorial Experiments

Random-Effects Model

Mixed-Effects Model

14.4 2k Factorial Experiments

Computational Techniques--Yates Method

14.5 2k Factorial Experiments in an Incomplete Block Design

14.6 Fractional Factorial Experiments

Chapter Summary

Exercises

Review Exercises

Chapter 15 Categorical Data

15.1 Multinomial Distribution

15.2 Chi-Squared Goodness of Fit Tests

15.3 Testing for Independence

r X c Test for Independence

15.4 Comparing Proportions

r X c Test for Homogeneity

Comparing Proportions with Paired Data: McNemar's Test

Chapter Summary

Exercises

Review Exercises

Chapter 16 Statistical Quality Control

16.1 Properties of Control Charts

Monitoring Means

Distribution of Run Lengths

16.2 Shewhart Control Charts for Measurements

X Chart (Mean)

R Chart (Range)

16.3 Shewhart Control Charts for Attributes

P Chart (Proportion Defective)

C Charts (Average Number of Defects)

16.4 Tolerance Limits

Two-Sided Tolerance Limits

Assumed Normal Distribution

One-Sided Tolerance Limits

Nonparametric Tolerance Interval

16.5 Acceptance Sampling

16.6 Two-Stage Acceptance Sampling

16.7 Extensions in Quality Control

Modifications of Control Charts

Parameter Design Procedures

Chapter Summary

Exercises

Appendixes

A Statistical Tables

B Answers to Selected Problems

C Selected Derivations

Index