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Half Title

Title

Statement

Copyright

Contents

Preface

Note to the Student

Ch 1: What Is Statistics?

1.1: Introduction

1.2: Characterizing a Set of Measurements: Graphical Methods

1.3: Characterizing a Set of Measurements: Numerical Methods

1.4: How Inferences Are Made

1.5: Theory and Reality

1.6: Summary

Ch 1: References and Further Readings

Ch 1: Supplementary Exercises

Ch 2: Probability

2.1: Introduction

2.2: Probability and Inference

2.3: A Review of Set Notation

2.4: A Probabilistic Model for an Experiment: The Discrete Case

2.5: Calculating the Probability of an Event: The Sample-Point Method

2.6: Tools for Counting Sample Points

2.7: Conditional Probability and the Independence of Events

2.8: Two Laws of Probability

2.9: Calculating the Probability of an Event: The Event-Composition Method

2.10: The Law of Total Probability and Bayes’ Rule

2.11: Numerical Events and Random Variables

2.12: Random Sampling

2.13: Summary

Ch 2: References and Further Readings

Ch 2: Supplementary Exercises

Ch 3: Discrete Random Variables and Their Probability Distributions

3.1: Basic Definition

3.2: The Probability Distribution for a Discrete Random Variable

3.3: The Expected Value of a Random Variable or a Function of a Random Variable

3.4: The Binomial Probability Distribution

3.5: The Geometric Probability Distribution

3.6: The Negative Binomial Probability Distribution (Optional)

3.7: The Hypergeometric Probability Distribution

3.8: The Poisson Probability Distribution

3.9: Moments and Moment-Generating Functions

3.10: Probability-Generating Functions (Optional)

3.11: Tchebysheff’s Theorem

3.12: Summary

Ch 3: References and Further Readings

Ch 3: Supplementary Exercises

Ch 4: Continuous Variables and Their Probability Distributions

4.1: Introduction

4.2: The Probability Distribution for a Continuous Random Variable

4.3: Expected Values for Continuous Random Variables

4.4: The Uniform Probability Distribution

4.5: The Normal Probability Distribution

4.6: The Gamma Probability Distribution

4.7: The Beta Probability Distribution

4.8: Some General Comments

4.9: Other Expected Values

4.10: Tchebysheff’s Theorem

4.11: Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)

4.12: Summary

Ch 4: References and Further Readings

Ch 4: Supplementary Exercises

Ch 5: Multivariate Probability Distributions

5.1: Introduction

5.2: Bivariate and Multivariate Probability Distributions

5.3: Marginal and Conditional Probability Distributions

5.4: Independent Random Variables

5.5: The Expected Value of a Function of Random Variables

5.6: Special Theorems

5.7: The Covariance of Two Random Variables

5.8: The Expected Value and Variance of Linear Functions of Random Variables

5.9: The Multinomial Probability Distribution

5.10: The Bivariate Normal Distribution (Optional)

5.11: Conditional Expectations

5.12: Summary

Ch 5: References and Further Readings

Ch 5: Supplementary Exercises

Ch 6: Functions of Random Variables

6.1: Introduction

6.2: Finding the Probability Distribution of a Function of Random Variables

6.3: The Method of Distribution Functions

6.4: The Method of Transformations

6.5: The Method of Moment-Generating Functions

6.6: Multivariable Transformations Using Jacobians (Optional)

6.7: Order Statistics

6.8: Summary

Ch 6: References and Further Readings

Ch 6: Supplementary Exercises

Ch 7: Sampling Distributions and the Central Limit Theorem

7.1: Introduction

7.2: Sampling Distributions Related to the Normal Distribution

7.3: The Central Limit Theorem

7.4: A Proof of the Central Limit Theorem (Optional)

7.5: The Normal Approximation to the Binomial Distribution

7.6: Summary

Ch 7: References and Further Readings

Ch 7: Supplementary Exercises

Ch 8: Estimation

8.1: Introduction

8.2: The Bias and Mean Square Error of Point Estimators

8.3: Some Common Unbiased Point Estimators

8.4: Evaluating the Goodness of a Point Estimator

8.5: Confidence Intervals

8.6: Large-Sample Confidence Intervals

8.7: Selecting the Sample Size

8.8: Small-Sample Confidence Intervals for μ and μ1 − μ2

8.9: Confidence Intervals for σ 2

8.10: Summary

Ch 8: References and Further Readings

Ch 8: Supplementary Exercises

Ch 9: Properties of Point Estimators and Methods of Estimation

9.1: Introduction

9.2: Relative Efficiency

9.3: Consistency

9.4: Sufficiency

9.5: The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation

9.6: The Method of Moments

9.7: The Method of Maximum Likelihood

9.8: Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional)

9.9: Summary

Ch 9: References and Further Readings

Ch 10: Supplementary Exercises

Ch 10: Hypothesis Testing

10.1: Introduction

10.2: Elements of a Statistical Test

10.3: Common Large-Sample Tests

10.4: Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests

10.5: Relationships Between Hypothesis-Testing Procedures and Confidence Intervals

10.6: Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Va

10.7: Some Comments on the Theory of Hypothesis Testing

10.8: Small-Sample Hypothesis Testing for μ and μ1 − μ2

10.9: Testing Hypotheses Concerning Variances

10.10: Power of Tests and the Neyman–Pearson Lemma

10.11: Likelihood Ratio Tests

10.12: Summary

Ch 10: References and Further Readings

Ch 10: Supplementary Exercises

Ch 11: Linear Models and Estimation by Least Squares

11.1: Introduction

11.2: Linear Statistical Models

11.3: The Method of Least Squares

11.4: Properties of the Least-Squares Estimators: Simple Linear Regression

11.5: Inferences Concerning the Parameters βi

11.6: Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression

11.7: Predicting a Particular Value of Y by Using Simple Linear Regression

11.8: Correlation

11.9: Some Practical Examples

11.10: Fitting the Linear Model by Using Matrices

11.11: Linear Functions of the Model Parameters: Multiple Linear Regression

11.12: Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression

11.13: Predicting a Particular Value of Y by Using Multiple Regression

11.14: A Test for H0: βg+1 = βg+2 = ··· = βk = 0

11.15: Summary and Concluding Remarks

Ch 11: References and Further Readings

Ch 11: Supplementary Exercises

Ch 12: Considerations in Designing Experiments

12.1: The Elements Affecting the Information in a Sample

12.2: Designing Experiments to Increase Accuracy

12.3: The Matched-Pairs Experiment

12.4: Some Elementary Experimental Designs

12.5: Summary

Ch 12: References and Further Readings

Ch 12: Supplementary Exercises

Ch 13: The Analysis of Variance

13.1: Introduction

13.2: The Analysis of Variance Procedure

13.3: Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout

13.4: An Analysis of Variance Table for a One-Way Layout

13.5: A Statistical Model for the One-Way Layout

13.6: Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional)

13.7: Estimation in the One-Way Layout

13.8: A Statistical Model for the Randomized Block Design

13.9: The Analysis of Variance for a Randomized Block Design

13.10 Estimation in the Randomized Block Design

13.11: Selecting the Sample Size

13.12: Simultaneous Confidence Intervals for More Than One Parameter

13.13: Analysis of Variance Using Linear Models

13.14: Summary

Ch 13: References and Further Readings

Ch 13: Supplementary Exercises

Ch 14: Analysis of Categorical Data

14.1: A Description of the Experiment

14.2: The Chi-Square Test

14.3: A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test

14.4: Contingency Tables

14.5: r × c Tables with Fixed Row or Column Totals

14.6: Other Applications

14.7: Summary and Concluding Remarks

Ch 14: References and Further Readings

Ch 14: Supplementary Exercises

Ch 15: Nonparametric Statistics

15.1: Introduction

15.2: A General Two-Sample Shift Model

15.3: The Sign Test for a Matched-Pairs Experiment

15.4: The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment

15.5: Using Ranks for Comparing Two Population Distributions: Independent Random Samples

15.6: The Mann–Whitney U Test: Independent Random Samples

15.7: The Kruskal–Wallis Test for the One-Way Layout

15.8: The Friedman Test for Randomized Block Designs

15.9: The Runs Test: A Test for Randomness

15.10: Rank Correlation Coefficient

15.11: Some General Comments on Nonparametric Statistical Tests

Ch 15: References and Further Readings

Ch 15: Supplementary Exercises

Ch 16: Introduction to Bayesian Methods for Inference

16.1: Introduction

16.2: Bayesian Priors, Posteriors, and Estimators

16.3: Bayesian Credible Intervals

16.4: Bayesian Tests of Hypotheses

16.5: Summary and Additional Comments

Ch 16: References and Further Readings

Appendix 1: Matrices and Other Useful Mathematical Results

Appendix 2: Common Probability Distributions, Means, Variances, and Moment-Generating Functions

Appendix 3: Tables

Answers

Index

BES-1

BES-2