OpenStax: Introduction to Statistics with R

This repository will detail R code solutions for the 2017 edition of OpenStax's Introduction to Statistics. Huge thanks to the authors, and to Rick Baraniuk for having the vision to place open-source, remixable textbooks online.

Table of Contents

1. Sampling and Data

• Definitions of Statistics, Probability, and Key Terms
• Data, Sampling, and Variation in Data and Sampling
• Frequency, Frequency Tables, and Levels of Measurement
• Experimental Design and Ethics
• Data Collection Experiment
• Sampling Experiment

2. Descriptive Statistics

• Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
• Histograms, Frequency Polygons, and Time Series Graphs
• Measures of the Location of the Data
• Box Plots
• Measures of the Center of the Data
• Skewness and the Mean, Median, and Mode
• Measures of the Spread of the Data
• Descriptive Statistics

3. Probability Topics

• Terminology
• Independent and Mutually Exclusive Events
• Two Basic Rules of Probability
• Contingency Tables
• Tree and Venn Diagrams
• Probability Topics

4. Discrete Random Variables

• Probability Distribution Function (PDF) for a Discrete Random Variable
• Mean or Expected Value and Standard Deviation
• Binomial Distribution
• Geometric Distribution
• Hypergeometric Distribution
• Poisson Distribution
• Discrete Distribution (Playing Card Experiment)
• Discrete Distribution (Lucky Dice Experiment)

5. Continuous Random Variables

• Continuous Probability Functions
• The Uniform Distribution
• The Exponential Distribution
• Continuous Distribution

6. The Normal Distribution

• The Standard Normal Distribution
• Using the Normal Distribution
• Normal Distribution (Lap Times)
• Normal Distribution (Pinkie Length)

7. The Central Limit Theorem

• The Central Limit Theorem for Sample Means (Averages)
• The Central Limit Theorem for Sums
• Using the Central Limit Theorem
• Central Limit Theorem (Pocket Change)
• Central Limit Theorem (Cookie Recipes)

8. Confidence Intervals

• A Single Population Mean using the Normal Distribution
• A Single Population Mean using the Student t Distribution
• A Population Proportion
• Confidence Interval (Home Costs)
• Confidence Interval (Place of Birth)
• Confidence Interval (Women's Heights)

9. Hypothesis Testing with One Sample

• Null and Alternative Hypotheses
• Outcomes and the Type I and Type II Errors
• Distribution Needed for Hypothesis Testing
• Rare Events, the Sample, Decision and Conclusion
• Additional Information and Full Hypothesis Test Examples
• Hypothesis Testing of a Single Mean and Single Proportion

10. Hypothesis Testing with Two Samples

• Two Population Means with Unknown Standard Deviations
• Two Population Means with Known Standard Deviations
• Comparing Two Independent Population Proportions
• Matched or Paired Samples
• Hypothesis Testing for Two Means and Two Proportions

11. The Chi-Square Distribution

• Facts About the Chi-Square Distribution
• Goodness-of-Fit Test
• Test of Independence
• Test for Homogeneity
• Comparison of the Chi-Square Tests
• Test of a Single Variance
• Lab 1: Chi-Square Goodness-of-Fit
• Lab 2: Chi-Square Test of Indepence

12. Linear Regression and Correlation

• Linear Equations
• Scatter Plots
• The Regression Equation
• Testing the Significance of the Correlation Coefficient
• Prediction
• Outliers
• Regression (Distance from School)
• Regression (Textbook Cost)
• Regression (Fuel Efficiency)

13. F Distribution and One-Way ANOVA

• One-Way ANOVA
• The F Distribution and the F-Ratio
• Facts About the F Distribution
• Test of Two Variances
• Lab: One-Way ANOVA

14. Review Exercises
15. Practice Tests (1-4) and Final Exams