This text covers the essential topics needed for a fundamental understanding of basic statistics and its applications in the fields of engineering and the sciences. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. The authors assume one semester of differential and integral calculus as a prerequisite.

1. Introduction to Statistics and Probability

1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability

1.2 Sampling Procedures; Collection of Data

1.3 Discrete and Continuous Data.

1.4 Probability: Sample Space and Events

            Exercises

1.5 Counting Sample Points

            Exercises

1.6 Probability of an Event

1.7 Additive Rules

            Exercises

1.8 Conditional Probability, Independence, and the Product Rule

            Exercises

1.9 Bayes' Rule

            Exercises

            Review Exercises

 

2. Random Variables, Distributions, and Expectations

2.1 Concept of a Random Variable

2.2 Discrete Probability Distributions

2.3 Continuous Probability Distributions

            Exercises

2.4 Joint Probability Distributions

            Exercises

2.5 Mean of a Random Variable

            Exercises

2.6 Variance and Covariance of Random Variables.

            Exercises

2.7 Means and Variances of Linear Combinations of Random Variables

            Exercises

            Review Exercises

2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

 

3. Some Probability Distributions

3.1 Introduction and Motivation

3.2 Binomial and Multinomial Distributions

            Exercises

3.3 Hypergeometric Distribution

            Exercises

3.4 Negative Binomial and Geometric Distributions

3.5 Poisson Distribution and the Poisson Process

            Exercises

3.6 Continuous Uniform Distribution

3.7 Normal Distribution

3.8 Areas under the Normal Curve

3.9 Applications of the Normal Distribution

            Exercises

3.10 Normal Approximation to the Binomial

            Exercises

3.11 Gamma and Exponential Distributions

3.12 Chi-Squared Distribution.

            Exercises

            Review Exercises

3.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

 

4. Sampling Distributions and Data Descriptions

4.1 Random Sampling

4.2 Some Important Statistics

            Exercises

4.3 Sampling Distributions

4.4 Sampling Distribution of Means and the Central Limit Theorem

            Exercises

4.5 Sampling Distribution of S₂

4.6 t-Distribution

4.7 F-Distribution

4.8 Graphical Presentation

            Exercises

            Review Exercises

4.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

 

5. One- and Two-Sample Estimation Problems

5.1 Introduction

5.2 Statistical Inference

5.3 Classical Methods of Estimation.

5.4 Single Sample: Estimating the Mean

5.5 Standard Error of a Point Estimate

5.6 Prediction Intervals

5.7 Tolerance Limits

            Exercises

5.8 Two Samples: Estimating the Difference between Two Means

5.9 Paired Observations

            Exercises

5.10 Single Sample: Estimating a Proportion

5.11 Two Samples: Estimating the Difference between Two Proportions

            Exercises

5.12 Single Sample: Estimating the Variance

            Exercises

            Review Exercises

5.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

 

6. One- and Two-Sample Tests of Hypotheses.

6.1 Statistical Hypotheses: General Concepts

6.2 Testing a Statistical Hypothesis

6.3 The Use of P-Values for Decision Making in Testing Hypotheses

            Exercises

6.4 Single Sample: Tests Concerning a Single Mean

6.5 Two Samples: Tests on Two Means

6.6 Choice of Sample Size for Testing Means

6.7 Graphical Methods for Comparing Means

            Exercises

6.8 One Sample: Test on a Single Proportion.

6.9 Two Samples: Tests on Two Proportions

            Exercises

6.10 Goodness-of-Fit Test

6.11 Test for Independence (Categorical Data)

6.12 Test for Homogeneity

6.13 Two-Sample Case Study

            Exercises

            Review Exercises

6.14 Potential Misconceptions and Hazards;

Relationship to Material in Other Chapters

 

7. Linear Regression

7.1 Introduction to Linear Regression

7.2 The Simple Linear Regression (SLR) Model and the Least Squares Method.

            Exercises

7.3 Inferences Concerning the Regression Coefficients.

7.4 Prediction

            Exercises

7.5 Analysis-of-Variance Approach

7.6 Test for Linearity of Regression: Data with Repeated Observations

            Exercises

7.7 Diagnostic Plots of Residuals: Graphical Detection of Violation of Assumptions

7.8 Correlation

7.9 Simple Linear Regression Case Study.

            Exercises

7.10 Multiple Linear Regression and Estimation of the Coefficients

            Exercises

7.11 Inferences in Multiple Linear Regression

            Exercises

            Review Exercises

 

8. One-Factor Experiments: General

8.1 Analysis-of-Variance Technique and the Strategy of Experimental Design

8.2 One-Way Analysis of Variance (One-Way ANOVA): Completely Randomized Design

8.3 Tests for the Equality of Several Variances

            Exercises

8.4 Multiple Comparisons

            Exercises

8.5 Concept of Blocks and the Randomized Complete Block Design

            Exercises

8.6 Random Effects Models

8.7 Case Study for One-Way Experiment

            Exercises

            Review Exercises

8.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

 

9. Factorial Experiments (Two or More Factors)

9.1 Introduction

9.2 Interaction in the Two-Factor Experiment

9.3 Two-Factor Analysis of Variance

            Exercises

9.4 Three-Factor Experiments.

            Exercises

            Review Exercises

9.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters