Introductory Statistics Study Guide

Exploring One-Variable Data

Describing distributions using center, spread, and shape with graphical and numerical summaries for categorical and quantitative data.

Exploring Two-Variable Data

Analyzing relationships between variables using scatterplots, correlation, and least-squares regression lines.

Collecting Data: Sampling Methods

Understanding sampling techniques, bias, and how sample design affects the validity of conclusions.

Collecting Data: Experimental Design

Designing experiments with randomization, replication, and control to establish cause-and-effect relationships between variables.

Probability Concepts and Rules

Applying addition, multiplication, and conditional probability rules to calculate probabilities of events and combinations.

Random Variables and Probability Distributions

Analyzing discrete and continuous random variables, calculating expected values, standard deviations, and combining random variables.

The Normal Distribution

Using normal models to calculate probabilities, find percentiles, and assess normality using the empirical rule.

Sampling Distributions

Understanding sampling variability, the Central Limit Theorem, and distributions of sample proportions and means.

Confidence Intervals for Proportions and Means

Constructing and interpreting confidence intervals while checking conditions and understanding margin of error.

Hypothesis Testing for Proportions and Means

Performing significance tests, interpreting p-values, and understanding Type I and Type II errors.

Inference for Two Samples and Paired Data

Comparing two populations using confidence intervals and hypothesis tests for differences in proportions and means.

Chi-Square Tests and Inference for Regression

Performing chi-square tests for categorical data and conducting inference for slope in linear regression models.