Module 1: Sampling and Data

# Course Contents at a Glance

Barbara Illowsky & OpenStax et al.

The following list shows a summary of the topics covered in this e-book.

## Module 1: Sampling and Data

- Definitions of Statistics, Probability, and Key Terms
- Sampling and Data
- Frequency, Frequency Tables, and Levels of Measurement
- Experimental Design and Ethics

## Module 2: Descriptive Statistics

- Stem-and-Leaf Graphs (Stemplots)
- Measures of the Location of the Data
- Histograms, Frequency Polygons, and Time Series Graphs
- Box Plots
- Measures of the Center of the Data
- Skewness and the Mean, Median, and Mode
- Measures of the Spread of Data
- When to use each measure of Central Tendency

**Module 3: Probability**

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

**Module 4: Discrete Random Variables**

- Probability Distribution Function (PDF) for a Discrete Random Variable
- Mean or Expected Value and Standard Deviation
- Binomial Distribution
- Geometric Distribution
- Poisson Distribution

**Module 5: Continuous Random Variables**

- Continuous Probability Functions
- The Uniform Distribution
- The Exponential Distribution

**Module 6: Normal Distribution**

- The Standard Normal Distribution
- Using the Normal Distribution

**Module 7: The Central Limit Theorem**

- The Central Limit Theorem for Sample Means (Averages)
- The Central Limit Theorem for Sums
- Using the Central Limit Theorem

**Module 8: Confidence Intervals**

- A Single Population Mean using the Normal Distribution
- A Single Population Mean using the Student Distribution
- A Population Proportion

**Module 9: Hypothesis Testing With One Sample**

- Null and Alternative Hypotheses
- Outcomes and the Type I and Type II Errors
- Distributions Needed for Hypothesis Testing
- Rare Events, the Sample, Decision and Conclusion
- Additional Informational and Full Hypothesis Test Examples

**Module 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

**Module 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

**Module 12: Linear Regression and Correlation**

- Linear Equations
- Scatter Plots
- The Regression Equation
- Testing the Significance of the Correlation Coefficient
- Prediction
- Outliers

**Module 13: F-Distribution and the One-Way ANOVA**

- One-Way ANOVA
- The F Distribution and the F-Ratio
- Facts about the F Distribution
- Test of Two Variances
- Relationships in an ANOVA Table

**Module 14: Multiple and Logistic Regression**

- Model Selection
- Checking Model Assumptions Using Graphs
- Line Fitting, Residuals, and Correlation
- Fitting a Line by Least Linear Regression
- Types of Outliers in Linear Regression
- Inference for Linear Regression