Put it all together: hypotheses, conditions, test statistic, p-value, and a conclusion in context. Change any input and the full four-step answer rewrites itself, so you can see exactly how each piece connects.
Enter the study details. The lab checks the conditions, does the calculations, and writes a full four-step answer (State, Plan, Do, Conclude) the way an AP grader wants to see it.
Write H₀ and Hₐ about p, define p in context, and give α.
One-sample z-test for p. Check Random, 10% (n ≤ 0.1N), and Large counts with p₀ (np₀ ≥ 10 and n(1 − p₀) ≥ 10).
z = (statistic − parameter) ÷ (SD of statistic) = (p̂ − p₀) ÷ √(p₀(1 − p₀)/n). It counts how many SDs p̂ is from p₀.
Find the area under the standard normal beyond z in the direction of Hₐ; double it for ≠.
"Because the p-value of 0.015 is less than α = 0.05, we reject H₀. There is convincing evidence that …"
The calculator gives z and p, but on the FRQ you must still show the formula with numbers and state the conditions.
The four steps and what graders look for in each.
| Step | What to write | Example |
|---|---|---|
| State | H₀, Hₐ, α, parameter in context | H₀: p = 0.10, Hₐ: p > 0.10, α = 0.05; p = true proportion of all students at the school who are left-handed |
| Plan | Procedure name and three conditions | One-sample z-test for p; random sample; 150 ≤ 240; 15 and 135 ≥ 10 |
| Do | p̂, z formula with numbers, p-value | p̂ = 0.1533; z = (0.1533 − 0.10)/0.0245 = 2.18; p = 0.0147 |
| Conclude | Compare p to α, decision, context | 0.0147 < 0.05, reject H₀; convincing evidence that more than 10% are left-handed |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 3.7. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 3 terminology guide.