Chapter Ⅰ Introduction to Statistics

1.1 Introduction

1.2 Data Collection and Descriptive Statistics

1.3 Inferential Statistics and Probability Models

1.4 Populations and Samples

1.5 A Brief History of Statistics

Problems

Chapter 2 Descriptive Statistics

2.1 Introduction

2.2 Describing Data Sets

2.2.1 Frequency Tables and Graphs

2.2.2 Relative Frequency Tables and Graphs

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

2.3 Summarizing Data Sets

2.3.1 Sample Mean，Sample Median，and Sample Mode

2.3.2 Sample Variance and Sample Standard Deviation

2.3.3 Sample Percentiles and Box Plots

2.4 Chebyshev’s Inequality

2.5 Normal Data Sets

2.6 Paired Data Sets and the Sample Correlation Coefficient

Problems

Chapter 3 Elements of Probability

3.1 Introduction

3.2 Sample Space and Events

3.3 Venn Diagrams and the Algebra of Events

3.4 Axioms of Probability

3.5 Sample Spaces Having Equally Likely Outcomes

3.6 Conditional Probability

3.7 Bayes’Formula

3.8 Independent Events

Problems

Chapter 4 Random Variables and Expectation

4.1 Random Variables

4.2 Types of Random Variables

4.3 Jointly Distributed Random Variables

4.3.1 Independent Random Variables

4.3.2 Conditional Distributions

4.4 Expectation

4.5 Properties of the Expected Value

4.5.1 Expected Value of Sums of Random Variables

4.6 Variance

4.7 Covariance and Variance of Sums of Random Variables

4.8 Moment Generating Functions

4.9 Chebyshev’s Inequality and the Weak Law of Large Numbers

Problems

Chapter 5 Special Random Variables

5.1 The Bernoulli and Binomial Random Variables

5.1.1 Computing the Binomial Distribution Function

5.2 The Poisson Random Variable

5.2.1 Computing the Poisson Distribution Function

5.3 The Hypergeometric Random Variable

5.4 The Uniform Random Variable

5.5 Normal Random Variables

5.6 Exponential Random Variables

5.6.1 The Poisson Process

5.7 The Gamma Distribution

5.8 Distributions Arising from the Normal

5.8.1 The Chi-Square Distribution

5.8.2 The t-Distribution

5.8.3 The F-Distribution

5.9 The Logistics Distribution

Problems

Chapter 6 Distributions of Sampling Statistics

6.1 Introduction

6.2 The Sample Mean

6.3 The Central Limit Theorem

6.3.1 Approximate Distribution of the Sample Mean

6.3.2 How Large a Sample Is Needed？

6.4 The Sample Variance

6.5 Sampling Distributions from a Normal Population

6.5.1 Distribution of the Sample Mean

6.5.2 Joint Distribution of X and S2

6.6 Sampling from a Finite Population

Problems

Chapter 7 Parameter Estimation

7.1 Introduction

7.2 Maximum Likelihood Estimators

7.2.1 Estimating Life Distributions

7.3 Interval Estimates

7.3.1 Confidence Interval for a Normal Mean When the Variance Is Unknown

7.3.2 Confidence Intervals for the Variance of a Normal Distribution

7.4 Estimating the Difference in Means of Two Normal Populations

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

7.6 Confidence Interval of the Mean of the Exponential Distribution

7.7 Evaluating a Point Estimator

7.8 The Bayes Estimator

Problems

Chapter 8 Hypothesis Testing

8.1 Introduction

8.2 Significance Levels

8.3 Tests Concerning the Mean of a Normal Population

8.3.1 Case of Known Variance

8.3.2 Case of Unknown Variance：The t-Test

8.4 Testing the Equality of Means of Two Normal Populations

8.4.1 Case of Known Variances

8.4.2 Case of Unknown Variances

8.4.3 Case of Unknown and Unequal Variances

8.4.4 The Paired t-Test

8.5 Hypothesis Tests Concerning the Variance of a Normal Population

8.5.1 Testing for the Equality of Variances of Two Normal Populations

8.6 Hypothesis Tests in Bernoulli Populations

8.6.1 Testing the Equality of Parameters in Two Bernoulli Populations

8.7 Tests Concerning the Mean of a Poisson Distribution

8.7.1 Testing the Relationship Between Two Poisson Parameters

Problems

Chapter 9 Regression

9.1 Introduction

9.2 Least Squares Estimators of the Regression Parameters

9.3 Distribution of the Estimators

9.4 Statistical Inferences About the Regression Parameters

9.4.1 Inferences Concerning β

9.4.2 Inferences Concerning α

9.4.3 Inferences Concerning the Mean Response α＋βx0

9.4.4 Prediction Interval of a Future Response

9.4.5 Summary of Distributional Results

9.5 The Coefficient of Determination and the Sample Correlation Coefficient

9.6 Analysis of Residuals：Assessing the Model

9.7 Transforming to Linearity

9.8 Weighted Least Squares

9.9 Polynomial Regression

9.10 Multiple Linear Regression

9.10.1 Predicting Future Responses

9.11 Logistic Regression Models for Binary Output Data

Problems

Chapter 10 Analysis of Variance

10.1 Introduction

10.2 An Overview

10.3 One-Way Analysis of Variance

10.3.1 Multiple Comparisons of Sample Means

10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes

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

10.5 Two-Factor Analysis of Variance：Testing Hypotheses

10.6 Two-Way Analysis of Variance with Interaction

Problems

Chapter Ⅱ Goodness of Fit Tests and Categorical Data Analysis

11.1 Introduction

11.2 Goodness of Fit Tests When All Parameters Are Specified

11.2.1 Determining the Critical Region by Simulation

11.3 Goodness of Fit Tests When Some Parameters Are Unspecified

11.4 Tests of Independence in Contingency Tables

11.5 Tests of Independence in Contingency Tables Having Fixed Marginal Totals

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

Problems

Chapter 12 Nonparametric Hypothesis Tests

12.1 Introduction

12.2 The Sign Test

12.3 The Signed Rank Test

12.4 The Two-Sample Problem

12.4.1 The Classical Approximation and Simulation

12.5 The Runs Test for Randomness

Problems

Chapter 13 Quality Control

13.1 Introduction

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

13.2.1 Case of Unknown μ and σ

13.3 S-Control Charts

13.4 Control Charts for the Fraction Defective

13.5 Control Charts for Number of Defects

13.6 Other Control Charts for Detecting Changes in the Population Mean

13.6.1 Moving-Average Control Charts

13.6.2 Exponentially Weighted Moving-Average Control Charts

13.6.3 Cumulative Sum Control Charts

Problems

Chapter 14 Life Testing

14.1 Introduction

14.2 Hazard Rate Functions

14.3 The Exponential Distribution in Life Testing

14.3.1 Simultaneous Testing——Stopping at the rth Failure

14.3.2 Sequential Testing

14.3.3 Simultaneous Testing—— Stopping by a Fixed Time

14.3.4 The Bayesian Approach

14.4 A Two-Sample Problem

14.5 The Weibull Distribution in Life Testing

14.5.1 Parameter Estimation by Least Squares

Problems

Chapter 15 Simulation，Bootstrap Statistical Methods，and Permutation Tests

15.1 Introduction

15.2 Random Numbers

15.2.1 The Monte Carlo Simulation Approach

15.3 The Bootstrap Method

15.4 Permutation Tests

15.4.1 Normal Approximations in Permutation Tests

15.4.2 Two-Sample Permutation Tests

15.5 Generating Discrete Random Variables

15.6 Generating Continuous Random Variables

15.6.1 Generating a Normal Random Variable

15.7 Determining the Number of Simulation Runs in a Monte Carlo Study

Problems

Appendix of Tables

Index