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Unit 3 · 15–25% of Exam

Inference for Categorical Data: Proportions

Your first taste of statistical inference. Using the sampling distribution of a sample proportion, you'll build confidence intervals and run significance tests for one and two population proportions, reason about Type I and Type II errors and power, and finish with chi-square tests for two-way tables.

15 topics
~30 class periods
15–25% of the exam
College Board aligned
← Back to AP Statistics

Choose your study tool

Six ways to master Unit 3 — pick whichever fits how you like to study.

Flashcards
24 interactive flashcards covering sampling distributions, confidence intervals, significance tests, errors and power, and chi-square tests. Tap to flip.
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Cheat Sheet
A one-page visual summary of Unit 3 — every condition, formula, and exam trap on a single screen.
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Essentials
The core concepts plus a searchable glossary of every vocabulary term you need to know for the exam.
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Visual Review
A slide-by-slide walkthrough of Unit 3 with sampling distributions, confidence intervals, test logic, and chi-square tables.
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MCQ Practice
35 multiple-choice questions in College Board exam style — with full explanations of every answer.
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FRQ Practice
A free-response question with model answers showing exactly how each part earns its point on the exam.
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Topics in Unit 3

All 15 topics from the College Board CED, in order.

Topic 3.1
Estimators
Point estimators and what makes a statistic a good estimator of a parameter.
Topic 3.2
Sampling Distributions for Sample Proportions
The mean, standard deviation, and shape of the distribution of p̂.
Topic 3.3
Constructing a Confidence Interval for a Population Proportion
The one-sample z-interval: estimate ± margin of error.
Topic 3.4
Justifying a Claim Based on a Confidence Interval
Using an interval to support or reject a claim about a proportion.
Topic 3.5
Setting Up a Test for a Population Proportion
Stating hypotheses and checking conditions for a proportion test.
Topic 3.6
Interpreting p-Values
What a p-value measures and how to interpret it in context.
Topic 3.7
Carrying Out a Test for a Population Proportion
The one-sample z-test statistic, p-value, decision, and conclusion.
Topic 3.8
Potential Errors When Performing Tests
Type I and Type II errors, their consequences, and the power of a test.
Topic 3.9
Sampling Distributions for the Difference Between Sample Proportions
The distribution of p̂₁ − p̂₂.
Topic 3.10
Constructing a Confidence Interval for the Difference Between Two Proportions
The two-sample z-interval for p₁ − p₂.
Topic 3.11
Justifying a Claim Based on a Two-Proportion Interval
Deciding whether two proportions plausibly differ.
Topic 3.12
Setting Up a Test for the Difference Between Two Proportions
Hypotheses and conditions, including the pooled proportion.
Topic 3.13
Carrying Out a Test for the Difference Between Two Proportions
The two-sample z-test statistic, p-value, and conclusion.
Topic 3.14
Setting Up a Chi-Square Test for Homogeneity or Independence
Hypotheses, expected counts, and conditions for a two-way table.
Topic 3.15
Carrying Out a Chi-Square Test for Homogeneity or Independence
The chi-square statistic, degrees of freedom, p-value, and conclusion.

About Unit 3

Unit 3 is where AP Statistics turns from describing data to drawing conclusions from it. Everything rests on the sampling distribution of a sample proportion p̂, which is approximately normal with mean p and standard deviation √(p(1−p)/n) when the conditions are met. From that foundation you build the two forms of inference: a confidence interval (estimate ± margin of error) that gives a plausible range for the true proportion, and a significance test that weighs evidence against a null hypothesis using a test statistic and a p-value.

You'll learn to state hypotheses, check the Random, 10%, and Large Counts conditions, interpret intervals and p-values in context, and reason carefully about Type I and Type II errors and the power of a test. The unit then extends every idea to two proportions (including the pooled proportion for tests) and closes with the chi-square test for homogeneity or independence, which compares distributions across the cells of a two-way table.

This unit is 15–25% of the AP Statistics exam and takes about 30 class periods. The four statistical practices below run through every topic:

Practice 1
Formulate Questions — pose a valid investigative question
Practice 2
Collect Data — identify the appropriate inference method
Practice 3
Analyze Data — compute intervals and test statistics
Practice 4
Interpret Results — justify conclusions in context
Up next
Unit 4: Inference for Quantitative Data: Means
Start Unit 4 →