AP Statistics · Unit 3 · Inference for Categorical Data: Proportions

97 AP-style multiple-choice questions and 8 free-response questions for AP Statistics · Unit 3 · Inference for Categorical Data: Proportions, sorted into 6 topics. Free sample questions for every topic.

6 topics97 multiple-choice8 free-response

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Topic 1 of 6

a significance test for a population proportion

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Question 1

A government analyst tests $H_0: p = 0.30$ vs. $H_a: p \neq 0.30$ with $\alpha = 0.05$ and obtains a p-value of $0.023$ from a sample of $n = 200$ . A colleague claims: "The p-value of $0.023$ means the probability we made a mistake is $2.3\%$ ." Which of the following explains why this statement is problematic?

Question 2

An environmental scientist tests whether more than 15 percent of the water samples a factory discharges are contaminated. In a random sample of 120 discharged samples, 25 were contaminated. The test gives a statistic of 1.79 and a p-value of 0.037, and the scientist had fixed the significance level at 0.01 before collecting data. What is the correct conclusion?

Sample free-response question

A town tests samples from its water supply. Each sample is either contaminated or not. The safe standard is that at most 5 percent of samples are contaminated. The town tests H0: p = 0.05 against Ha: p > 0.05 every month.

(a) Describe a Type I error and a Type II error in this context.
(b) Which error is more serious for the town's residents? Explain.
(c) Should the town use a significance level of 0.01 or 0.10? Explain using part (b).
(d) Describe two ways the town could increase the power of its test.
(e) The test has power 0.70 if the true rate is 8 percent. Interpret this value.

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Full practice for AP Statistics · Unit 3 · Inference for Categorical Data: Proportions: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts

Part a1 / 1 pts

Point 1: Earned

94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts

Point 1: Earned

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

AP Statistics · Unit 3 · Inference for Categorical Data: Proportions Practice Questions | S&D Academy