AP Biology / AP Statistics · Unit 4
Unit 4: Inference for Quantitative Data — Means
Unit 4 is 10–20% of the AP Statistics exam and covers all t-procedures. Every question hinges on the same four-step template as Unit 3 — but the sampling distribution is t (with degrees of freedom), and the Normal condition depends on sample size.
Weight and scope
Exam weight: 10–20%. FRQ 3 (Inference focus) is a t-procedure roughly half the time.
Procedures you must know
| Question | Procedure |
|---|---|
| Estimate one population mean | 1-sample t-interval |
| Test a claim about one mean | 1-sample t-test |
| Compare two independent means | 2-sample t-interval / t-test |
| Compare paired measurements from the same subjects | Matched-pairs t-interval / t-test on the differences |
The four-step template (means edition)
- State. Define μ (or μ1 − μ2) in context; state H₀ and Hₐ; state α.
- Plan. Name the procedure (e.g., "2-sample t-test for a difference in means"). Check Random, 10%, and Normal / Large Sample.
- Do. Report t, df, and p-value (or the interval). Cite the calculator output — no need to reproduce the standard error by hand.
- Conclude. Compare p to α, reject / fail to reject, then answer the actual question in context.
Conditions per procedure
| Procedure | Random | Independence | Normal / Large Sample |
|---|---|---|---|
| 1-sample t | Yes | n ≤ 0.10N if sampling without replacement | n ≥ 30, or population normal, or plot roughly symmetric with no outliers |
| 2-sample t | Both random | Both n ≤ 0.10N | Same rule applied to each sample individually |
| Matched-pairs t | Pairs randomly assigned or subjects randomly selected | Pairs independent | Rule applied to the sample of differences |
Matched pairs is a 1-sample procedure
The single most-missed idea in Unit 4: matched pairs is a 1-sample t on the differences, not a 2-sample test. Compute the differences first, then run the 1-sample t-interval or t-test on that new list. The parameter is μd, the mean difference.
Calculator moves
- T-Test, T-Interval, 2-SampTTest, 2-SampTInt — read t, df, and p-value directly.
- For matched pairs, store the differences in a list first, then use T-Test / T-Interval on that list.
- In Bluebook Desmos, use
tdist(df).cdf(t)for a one-sided p-value.
Common mistakes
- Using a z-procedure when σ is unknown.
- Running a 2-sample test when the design is matched pairs.
- Skipping the Normal condition on small-sample FRQs — you must plot the data and describe it.
- Writing "the mean difference is 0" as your conclusion instead of an answer in context.
FAQ
When do I use a matched-pairs t-test vs. a 2-sample t-test?
Use a matched-pairs t-test when each subject (or naturally paired subjects) provides two related measurements — before/after, twin studies, or paired designs. Use a 2-sample t-test when the two samples are independent. Matched pairs analyzes the differences as a single sample.
How do I know if the Normal condition is met for a t-procedure?
If n ≥ 30 the CLT covers you. If 15 ≤ n < 30, the sample must be roughly symmetric with no strong skew or outliers. If n < 15, the sample must look approximately normal (roughly symmetric, no outliers). Always show the plot on an FRQ.
Keep going
Practice t-procedures until the template is automatic.
Cramapple's Unit 4 practice sets score every rubric criterion — parameter, hypotheses, conditions, statistic, and conclusion — so you know exactly which sentence needs work.
One-time purchase. No subscription.