AP Statistics / Inference for Quantitative Data: Means
Lesson
Interpreting tests about a mean
State a claim about μ, then let the sample mean argue with it.
Learning goals
- Write hypotheses for a mean in symbols and words.
- Distinguish paired differences from two independent groups.
Explanation
A test about a mean asks whether the population average could still be the claimed value. The t-statistic counts how many standard errors the sample mean sits from that claim. Context decides whether you care about greater, less, or different.
Two designs get mixed up. Independent groups compare two separate samples. Paired data come in matched pairs or before-after measurements; you subtract first and test the mean difference. Using the wrong design misstates both the sample size and the variability.
Key terms
- Null hypothesis. The statement about a parameter that the test assumes for the sake of measuring surprise.
- Paired data. Measurements linked in pairs so that the meaningful variable is the difference within each pair.
Common mistakes
- Writing hypotheses about the sample mean instead of the population mean.
- Running a two-sample t-test on before-and-after scores from the same people.
Practice
Original Marlow Works items. Check the answer explanation after you try.
A reporter stands at one grocery-store exit and asks shoppers whether they support a new park tax. Why is this a poor way to estimate citywide support?
Original Marlow Works item — not a College Board question.
Take your time—this is practice, not a test.
Answer explanation
A coach claims the team’s mean free-throw percentage is 70. A random sample of 12 players has mean 64. What is H0?
Answer. H0: μ = 70, where μ is the team’s true mean free-throw percentage.
Hypotheses are about the population parameter, not about the sample mean of 64.
Related resources
External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.
Official / link only
AP Statistics course page
Official revised 2026–27 five-unit framework.
College Board · All rights reserved · accessed 2026-10-01
Open sourceCC BY — attribution required
Collaborative Statistics
Open statistics text for distributions, probability, and inference.
Open Textbook Library listing · CC BY · accessed 2026-10-01
Open source