A student wants to perform a significance test to compare the proportion of two independent random samples who support a proposed zoning change: 14 of 60 residents in Neighborhood 1 and 9 of 55 residents in Neighborhood 2. Before performing the test, the student must check the large counts condition using the pooled proportion, which is . Which of the following correctly evaluates this condition?
inference for the difference of two proportions
Review inference for the difference of two proportions for AP Statistics and try 2 free AP-style practice questions. 19 questions on this topic in AP Statistics · Unit 3 · Inference for Categorical Data: Proportions.
6 topics97 multiple-choice8 free-response
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A factory operates two production lines that use different machinery to assemble the same product. A quality control manager took independent random samples of items from each line and performed a two-proportion z-test comparing the proportion of defective items produced by each line. The test produced a p-value of 0.018, and the manager wants to explain to the plant supervisor exactly what this p-value represents. Which of the following is a correct interpretation?
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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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
Grader confidence 94% sureReason: 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
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."