Elementary Statistics

Ron Larson received his PhD in mathematics from the University of Colorado in 1970. At that time he accepted a position with Penn State University, and he currently holds the rank of professor of mathematics at the University. Dr. Larson is the lead author of more than two dozen mathematics textbooks that range from sixth grade through calculus levels.   Betsy Farber received her Bachelor's degree in mathematics form Penn State University and Master's degree in mathematics from the College of New Jersey. Since 1976, she has been teaching all levels of mathematics at Bucks County Community College in Newton, Pennsylvania, where she currently holds the rank of professor. She is particularly interested in developing new ways to make statistics relevant and interesting to her students and has been teaching statistics in many different modes - with TI-83/84, with MINITAB, and by distance learning as well as in the traditional classroom.

Part One. Descriptive Statistics

 

1. Introduction to Statistics

1.1. An Overview of Statistics

1.2. Data Classification

1.3. Data Collection and Experimental Design

 

2. Descriptive Statistics

2.1. Frequency Distributions and Their Graphs

2.2. More Graphs and Displays

2.3. Measures of Central Tendency

2.4. Measures of Variation

2.5. Measures of Position

 

Part Two. Probability & Probability Distributions

 

3. Probability

3.1. Basic Concepts of Probability and Counting

3.2. Conditional Probability and the Multiplication Rule

3.3. The Addition Rule

3.4. Additional Topics in Probability and Counting

 

4. Discrete Probability Distributions

4.1. Probability Distributions

4.2. Binomial Distributions

4.3. More Discrete Probability Distributions

 

5. Normal Probability Distributions

5.1. Introduction to Normal Distributions and the Standard Normal Distribution

5.2. Normal Distributions: Finding Probabilities

5.3. Normal Distributions: Finding Values

5.4. Sampling Distributions and the Central Limit Theorem

5.5. Normal Approximations to Binomial Distributions

 

Part Three. Statistical Inference

 

6. Confidence Intervals

6.1. Confidence Intervals for the Mean (Large Samples)

6.2. Confidence Intervals for the Mean (Small Samples)

6.3. Confidence Intervals for Population Proportions

6.4. Confidence Intervals for Variance and Standard Deviation

 

7. Hypothesis Testing with One Sample

7.1. Introduction to Hypothesis Testing

7.2. Hypothesis Testing for the Mean (Large Samples)

7.3. Hypothesis Testing for the Mean (Small Samples)

7.4. Hypothesis Testing for Proportions

7.5. Hypothesis Testing for Variance and Standard Deviation

 

8. Hypothesis Testing with Two Samples

8.1. Testing the Difference Between Means (Large Independent Samples)

8.2. Testing the Difference Between Means (Small Independent Samples)

8.3. Testing the Difference Between Means (Dependent Samples)

8.4. Testing the Difference Between Proportions

 

Part Four. More Statistical Inference

 

9. Correlation and Regression

9.1 Correlation

9.2. Linear Regression

9.3. Measures of Regression and Prediction Intervals

9.4. Multiple Regression

 

10. Chi-Square Tests and the F-Distribution

10.1. Goodness-of-Fit Test

10.2. Independence

10.3. Comparing Two Variances

10.4. Analysis of Variance

 

11. Nonparametric Tests

11.1. The Sign Test

11.2. The Wilcoxon Tests

11.3. The Kruskal-Wallis Test

11.4. Rank Correlation

11.5. The Runs Test

 

Appendix A. Alternative Presentation of the Standard Normal Distribution

            Standard Normal Distribution Table (0-to-z)

            Alternative Presentation of the Standard Normal Distribution

Appendix B. Tables

            Table 1 Random Numbers

            Table 2 Binomial Distribution

            Table 3 Poisson Distribution

            Table 4 Standard Normal Distribution

            Table 5 t-Distribution

            Table 6 Chi-Square Distribution

            Table 7 F-Distribution

            Table 8 Critical Values for the Sign Test

            Table 9 Critical Values for the Wilcoxon Signed-Rank Test

            Table 10 Critical Values for the Spearman Rank Correlation

            Table 11 Critical Values for the Pearson Correlation Coefficient

            Table 12 Critical Values for the Number of Runs

Appendix C. Normal Probability Plots and Their Graphs

 

Answers to the Try It Yourself Exercises

Odd Answers

Index

Photo Credits