An environmental scientist reports a 95 percent confidence interval for the difference between two population means as . A colleague wants to test, at the 0.05 level, whether that difference equals 5. Which of the following conclusions follows from the interval?
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 4 · Inference for Quantitative Data: Means.
4 topics54 multiple-choice8 free-response
Try free questions
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?
Sample free-response question
A nutrition researcher is planning four studies about sodium in diets.
(a) Study 1 measures sodium intake of 50 randomly selected adults and compares the mean with the recommended 2,300 mg. Identify the procedure and explain.
(b) Study 2 measures the same 40 adults before and after a month of a low-salt diet. Identify the procedure and explain.
(c) Study 3 randomly assigns 60 adults to a low-salt diet or a usual diet and compares mean blood pressure. Identify the procedure and explain.
(d) Study 4 records whether each of 200 adults exceeds 2,300 mg. Explain why a t procedure is not appropriate.
(e) Which of the four studies could support a cause-and-effect conclusion about diet? Explain.
6 more questions on this topic
Full practice for AP Statistics · Unit 4 · Inference for Quantitative Data: Means: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.
Start practicing freeInside the course
How practice works on S&D Academy
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."