AP Biology / AP Statistics · Unit 3
Unit 3: Inference for Categorical Data — Proportions
Unit 3 is 15–25% of the AP Statistics exam and is the first inference unit. The redesign removed chi-square goodness-of-fit but kept 1- and 2-proportion procedures and chi-square tests for independence and homogeneity. Expect an inference procedure on FRQ 3 and often as the core of FRQ 4.
Weight and scope
Exam weight: 15–25%. FRQ 3 is dedicated to an inference procedure — about half the time, that procedure is from this unit.
Procedures you must know
| Question | Procedure |
|---|---|
| Estimate a single population proportion | 1-proportion z-interval |
| Test a claim about a single proportion | 1-proportion z-test |
| Compare two population proportions | 2-proportion z-interval |
| Test whether two proportions differ | 2-proportion z-test (pooled p̂) |
| Test whether two categorical variables are associated within one sample | Chi-square test for independence |
| Test whether the distribution of one categorical variable is the same across ≥2 populations | Chi-square test for homogeneity |
The four-step inference template
- State. Parameter(s) in context, hypotheses, significance level.
- Plan. Name the procedure and check its conditions (Random, 10%, Large Counts).
- Do. Compute the test statistic and p-value (or interval); cite df for chi-square.
- Conclude. Compare p to α, reject or fail to reject H₀, and answer the original question in context.
Every AP grader is trained on this template. If you skip a step, you skip a rubric point. See our FRQ tips guide for phrasing.
Conditions per procedure
| Procedure | Random | Independence | Normal / Large Counts |
|---|---|---|---|
| 1-proportion z-test | Yes | n ≤ 0.10N | np₀ ≥ 10 and n(1−p₀) ≥ 10 |
| 1-proportion z-interval | Yes | n ≤ 0.10N | np̂ ≥ 10 and n(1−p̂) ≥ 10 |
| 2-proportion z-test | Both random | Both n ≤ 0.10N | n₁p̂c, n₁(1−p̂c), n₂p̂c, n₂(1−p̂c) all ≥ 10 |
| Chi-square (indep./homog.) | Yes | n ≤ 0.10N per sample | All expected counts ≥ 5 |
Chi-square procedures
- Test for independence — one sample, two categorical variables recorded per subject. H₀: the two variables are independent in the population.
- Test for homogeneity — two or more independent samples, one categorical variable each. H₀: the distribution of that variable is the same across the populations.
- Expected count formula: (row total × column total) / grand total. Degrees of freedom: (rows − 1)(columns − 1).
- If the chi-square test rejects, follow up by comparing observed vs. expected in the cells that contributed the largest components — the FRQ often asks which cells drove the result.
Common mistakes
- Using the sample proportion p̂ in the Large Counts check for a test (should be p₀).
- Forgetting to pool p̂ for a 2-proportion z-test.
- Confusing chi-square for independence with chi-square for homogeneity.
- Concluding "the proportions are equal" after failing to reject H₀. You never accept H₀ — you fail to reject.
FAQ
Is chi-square goodness-of-fit still tested?
No. The 2026–27 CED removed chi-square goodness-of-fit (old Topics 8.2 and 8.3). Chi-square tests for independence and homogeneity remain in Unit 3.
What conditions do I check for a 1-proportion z-test?
Random sample or random assignment; 10% condition if sampling without replacement (n ≤ 10% of population); Large Counts using the null value p₀: np₀ ≥ 10 and n(1 − p₀) ≥ 10. For a confidence interval, use p̂ instead of p₀ in the Large Counts check.
Keep going
Nail every rubric point on inference FRQs.
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