AP Statistics — comparing two proportions

This material trains the part of Unit 3 of the AP Statistics course framework for 2026–27 that compares two groups on a categorical outcome: inference for the difference between two population proportions. It is written for students preparing for the May 2027 exam at introductory college level, with a graphing calculator at hand.

The quiz covers the whole procedure one skill at a time. You find the mean and standard deviation of the sampling distribution of a difference in sample proportions; spot a failed normality condition when one group has too few successes; compute a two-sample z-interval from survey counts; use an interval that lies entirely on the positive side of zero, and one that contains zero, to judge whether two proportions differ; write hypotheses for a randomized experiment; compute a pooled proportion when the two samples have different sizes and use it in the test statistic; check the normality condition for a test with the pooled proportion; interpret a p-value; state a conclusion with the cause-and-effect scope that random assignment allows; and choose the change that raises the power of a test. Each question carries its own numbers, and every explanation shows the working and why the other answers are wrong.

The flashcards collect the formulas, the difference between the conditions for an interval and for a test, the reason for pooling, and the rules for reading intervals and stating the scope of conclusions.

The written work is a printable sheet of eight free-response tasks in the style of the exam's inference question: a complete two-proportion interval that turns out to contain zero, a complete two-proportion test for an experiment, why tests pool and intervals do not, a probability from the sampling distribution of a difference, conditions for samples versus experiments, interpreting and judging an interval for a website change, Type I and Type II errors with ways to raise power, and a critique of a causal claim drawn from a survey. Handwritten answers are photographed and checked against model answers and key points.

The oral exam has an examiner ask one question at a time about a comparison of two proportions, from choosing the procedure to stating the conclusion and its scope, and it ends with short, precise feedback.

Chi-square tests for homogeneity and independence, which compare more than two categories, are covered by a separate material of this category. All scenarios are invented and all questions are original practice items written by Zestly, not released exam questions. The material follows the published course framework but is independent practice and does not predict an exam score.

• Describe the sampling distribution of a difference between two sample proportions
• Check the randomization, 10% and normality conditions for two-proportion intervals and tests
• Construct and interpret a two-sample z-interval for $p_1 - p_2$ and use it to judge whether proportions differ
• Compute a pooled proportion and a two-sample z test statistic, and interpret the p-value
• State conclusions with the correct scope for experiments and for random samples
• Describe Type I and Type II errors and the factors that increase power

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 3, Inference for Categorical Data: Proportions, topics 3.9–3.13). Original questions, not released exam items.