a significance test for a population proportion

Review a significance test for a population proportion for AP Statistics and try 2 free AP-style practice questions. 20 questions on this topic in AP Statistics · Unit 6 · Inference for Categorical Data: Proportions.

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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?

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Full practice for AP Statistics · Unit 6 · 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."

A significance test for a population proportion: AP Statistics Practice Questions | S&D Academy