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inference for the difference of two means

Review inference for the difference of two means for AP Statistics and try 2 free AP-style practice questions. 8 questions on this topic in AP Statistics · Unit 7 · Inference for Quantitative Data: Means.

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Question 1

An environmental scientist reports a 95 percent confidence interval for the difference between two population means as (−2.1, 8.7)(-2.1,\ 8.7). A colleague wants to test, at the 0.05 level, whether that difference equals 5. Which of the following conclusions follows from the interval?

Question 2

Researchers compared healing time, in days, after two surgical techniques. A random sample of 15 patients treated with the first technique had a mean of 12.4 days and a standard deviation of 3.1 days; an independent random sample of 18 patients treated with the second had a mean of 10.8 days and a standard deviation of 4.6 days. Using a conservative critical value of 2.145, which of the following is a 95 percent confidence interval for the difference in mean healing time?

6 more questions on this topic

Full practice for AP Statistics · Unit 7 · Inference for Quantitative Data: Means: 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
Grader confidence 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
Grader confidence 91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned
Grader confidence 88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned
Grader confidence 82% sure

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

Evidence: "Revenue goes down."

Inference for the difference of two means: AP Statistics Practice Questions | S&D Academy