matched pairs and paired data

Review matched pairs and paired data for AP Statistics and try 2 free AP-style practice questions. 14 questions on this topic in AP Statistics · Unit 4 · Inference for Quantitative Data: Means.

4 topics54 multiple-choice8 free-response

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Question 1

A winemaker wants to know whether aging in oak barrels raises the quality rating of a Chardonnay. She rated each of 10 batches of wine before aging and again after six months of aging, then computed the difference, after minus before, for each batch: 3, 1, 4, 2, $-1$ , 5, 2, 3, 1, 4. Which of the following gives appropriate hypotheses together with the mean and standard deviation of the differences?

Question 2

An economist formed 18 matched pairs of cities, alike in population, median income and region, and put one program in one city of each pair and a second program in the other. For the 18 differences in unemployment reduction, the mean was $-0.42$ percentage point and the standard deviation was 1.18 percentage points. She tests whether the mean difference is 0, using a critical value of 2.110 with 17 degrees of freedom. What is the value of the test statistic, and what is the conclusion?

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.

12 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.

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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."

Matched pairs and paired data: AP Statistics Practice Questions | S&D Academy