Unit 1: Exploring One-Variable Data

Summary Statistics

Describing Variables

Parameters & Statistics

Measures of Center

Measures of Position

Measures of Variability

Tables & Relative Frequency

Grouped Data

Outliers & Resistant Measures

Five-Number Summary & Boxplots

Skewness of Data

Comparing Data using Summary Statistics

Graphical Representations

Shape of Distributions

Bar Charts & Histograms

Dotplots & Stemplots

Cumulative Graphs

Comparing Univariate Graphs

The Normal Distribution

Properties of Normal Distributions

Standardized z-scores

Comparing Normal Distributions

Finding Proportions from Normal Distributions

Inverse Normal Calculations

Estimating Parameters of Normal Distributions

Unit 2: Exploring Two-Variable Data

Tables & Graphs

Two-Way Tables & Relative Frequencies

Bar Graphs & Mosaic Plots

Scatterplots & Regression

Explanatory & Response Variables

Scatterplots

Association & Correlation Coefficients

Interpolation & Extrapolation using Linear Models

Residuals

The Least-Squares Regression Line

Residual Plots

The Coefficient of Determination

Outliers, High-Leverage & Influential Points

Linearization of Bivariate Data

Unit 3: Collecting Data

Sampling Methods & Bias

Introduction to Sampling

Simple Random Sampling (SRS)

Random Sampling Methods

Types of Bias

Non-random (Biased) Sampling Methods

Experimental Design

Introduction to Experiments

Well-Designed Experiments

Control Groups, Placebos & Blind Experiments

Completely Randomized Design

Randomized Block & Matched Pairs Design

Unit 4: Probability, Random Variables & Probability Distributions

Probability

Estimating Probability using Relative Frequency

Probabilities of Single Events

Introduction to Combined Events

Addition Rule & Mutually Exclusive Events

Conditional Probability

Multiplication Rule & Independent Events

Probabilities of Combined Events using Tree Diagrams

Probabilities of Combined Events using the Rules

Discrete Random Variables

Probability Distributions for Discrete Random Variables

Cumulative Probability Distributions for Discrete Random Variables

Mean & Standard Deviation of a Discrete Random Variable

Linear Transformations of Random Variables

Linear Combinations of Random Variables

Binomial & Geometric Distributions

Introduction to Binomial Distributions

Probabilities for Binomial Distributions

Introduction to Geometric Distributions

Probabilities for Geometric Distributions

Unit 5: Sampling Distributions

Sampling Distributions

Introduction to Sampling Distributions

Sampling Distributions for Sample Means

The Central Limit Theorem

Sampling Distributions for Differences in Sample Means

Sampling Distributions for Sample Proportions

Sampling Distributions for Differences in Sample Proportions

Biased & Unbiased Estimators

Units 6-9: Inference

Introduction to Inference

Tails on a Normal Distribution

Introduction to Hypothesis Testing

Introduction to Confidence Intervals

Inference for Proportions

Hypothesis Tests for Population Proportions

Confidence Intervals for Population Proportions

Hypothesis Tests for Differences in Population Proportions

Confidence Intervals for Differences in Population Proportions

Inference for Means

The t-distribution

Hypothesis Tests for Population Means

Confidence Intervals for Population Means

Hypothesis Tests for Differences in Population Means

Confidence Intervals for Differences in Population Means

t-scores versus z-scores

Hypothesis Tests for Differences in Matched Pairs

Confidence Intervals for Differences in Matched Pairs

Goodness of Fit (Chi-Square)

The Chi-Square Distribution

Hypothesis Tests for Goodness of Fit

Independence & Homogeneity (Chi-Square)

Tests for Independence

Tests for Homogeneity

Inference for Regression Slopes

Sampling Distributions for Sample Slopes

Hypothesis Tests for Slopes of Regression Lines

Confidence Intervals for Slopes of Regression Lines

Errors in Hypothesis Tests

Type I & Type II Errors

Probabilities of Errors

Power of a Test