A statistics teacher plans a test about a population proportion with a fixed significance level and a fixed sample size. She first considers a two-sided alternative and then considers a one-sided alternative in the direction she expects the proportion to move. How does the power of the test against that alternative change?
potential errors when performing tests
Review potential errors when performing tests for AP Statistics and try 2 free AP-style practice questions. 15 questions on this topic in AP Statistics · Unit 3 · Inference for Categorical Data: Proportions.
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A traffic safety officer tests whether more than 40% of teen drivers text while driving (, , , n = 250). The true proportion who text is 43%. Which of the following correctly describes the relationship between power and Type II error in this study?
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.
13 more questions on this topic
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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."