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.

(NOTE: Each chapter begins with Where You’ve Been and Where You're Going sections and concludes with Uses and Abuses, Chapter Summary, Review Exercises, Chapter Quiz, Real Statistics-Real Decisions—Putting it all Together, and Technology sections.)


1. Introduction to Statistics.

An Overview of Statistics. Data Classification. Case Study: Rating Television Shows in the United States. Experimental Design.

 

2. Descriptive Statistics.

Frequency Distributions and Their Graphs. More Graphs and Displays. Measures of Central Tendency. Measures of Variation. Case Study: Earnings of Athletes. Measures of Position.

 

3. Probability.

Basic Concepts of Probability. Conditional Probability and the Multiplication Rule. The Addition Rule. Case Study: Probability and Parking Lot Strategies. Additional Topics in Probability and Counting.

 

4. Discrete Probability Distributions.

Probability Distributions. Binomial Distributions. Case Study: Binomial Distribution of Airplane Accidents. More Discrete Probability Distributions.

 

5. Normal Probability Distributions.

Introduction to Normal Distributions and the Standard Normal Distribution. Normal Distributions: Finding Probabilities. Normal Distributions: Finding Values.

Case Study: Birth Weights in America. Sampling Distributions and The Central Limit Theorem. Normal Approximations to Binomial Distributions.

 

6. Confidence Intervals.

Confidence Intervals for the Mean (Large Samples). Case Study: Shoulder Heights of Appalachian Black Bears. Confidence Intervals for the Mean (Small Samples). Confidence Intervals for Population Proportions. Confidence Intervals for Variance and Standard Deviation.

 

7. Hypothesis Testing with One Sample

Introduction to Hypothesis Testing. Hypothesis Testing for the Mean (Large Samples). Case Study: Human Body Temperature: What's Normal? Hypothesis Testing for the Mean (Small Samples). Hypothesis Testing for Proportions. Hypothesis Testing for the Variance and Standard Deviation.

 

8. Hypothesis Testing with Two Samples.

Testing the Difference Between Means (Large Independent Samples). Case Study: Oatbran and Cholesterol Level. Testing the Difference Between Means (Small Independent Samples). Testing the Difference Between Means (Dependent Samples). Testing the Difference Between Proportions.

 

9. Correlation and Regression.

Correlation. Linear Regression. Case Study: Correlation of Body Measurements. Measures of Regression and Prediction Intervals. Multiple Regression.

 

10. Chi-Square Tests and the F-Distribution.

Goodness of Fit. Independence. Case Study: Traffic Safety Facts. Comparing Two Variances. Analysis of Variance.

 

11. Nonparametric Tests.

The Sign Test. The Wilcoxon Tests. Case Study: Health and Nutrition. The Kruskal-Wallis Test. Rank Correlation. Runs Test.

 

Appendix A.

Alternative Presentation of the Standard Normal Distribution. Standard Normal Distribution Table (0-to-z). Alternate Presentation of the Standard Normal Distribution.

 

Appendix B.

Tables.