AP Statistics — chi-square tests for homogeneity and independence

This material trains the last two topics of Unit 3 of the AP Statistics course framework for 2026–27: chi-square tests for homogeneity and for independence in two-way tables. It is written for students preparing for the May 2027 exam at introductory college level, with a graphing calculator at hand. In the revised framework these two tests are the chi-square procedures that remain, so the material concentrates on telling them apart and carrying them out completely.

The quiz takes one skill per question. You decide from the design of a study whether it calls for a test for homogeneity (several samples or treatment groups, one categorical variable) or for independence (one sample, two categorical variables); write the hypotheses for each in context; compute an expected count from the row, column and table totals; find the degrees of freedom of a two-way table; compute a chi-square statistic from observed and expected counts; check the expected counts condition, under which every expected count must be greater than 5; read a p-value from a statistic and its degrees of freedom; interpret that p-value; state a conclusion that speaks of association rather than causation for an observational study; and use the cell contributions to say where a significant difference comes from. Every explanation shows the arithmetic and why the other answers fail.

The flashcards summarize the two tests, their hypotheses and data designs, the formulas for expected counts, the statistic and the degrees of freedom, the conditions, and what a chi-square result does and does not tell you.

The written work is a printable sheet of eight free-response tasks in the style of the exam's inference question: a complete test for independence from a table, a complete test for homogeneity for three cities, the difference between the two tests, the meaning of an expected count, the shape of chi-square distributions and why only the upper tail counts, a table that fails the expected counts condition, a full interpretation for a randomized experiment, and the limits of a significant result. 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 two-way table, from choosing the test to following up a significant result, and it ends with short, precise feedback.

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.

• Choose between a chi-square test for homogeneity and a test for independence from the design of a study
• State hypotheses for both tests in context
• Compute expected counts, the chi-square statistic and its degrees of freedom
• Check the randomization, 10% and expected counts conditions
• Interpret a p-value and state a conclusion with the correct scope
• Use cell contributions to describe where a significant difference comes from

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 3.14–3.15). Original questions, not released exam items.