2024 AP Statistics Free-Response Questions
Advanced PlacementAP StatisticsFree ResponseMathematics
6 questions24 pts
6 gradable24 rubric criteria0 dependencies
q1Question 1
q1
Question 1
Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. A large exercise center has several thousand members from age 18 to 55 years and several thousand members age 56 and older. The manager of the center is considering offering online fitness classes. The manager is investigating whether members’ opinions of taking online fitness classes differ by age. The manager selected a random sample of 170 exercise center members ages 18 to 55 years and a second random sample of 230 exercise center members ages 56 years and older. Each sampled member was asked whether they would be interested in taking online fitness classes. The manager found that 51 of the 170 sampled members ages 18 to 55 years and that 79 of the 230 sampled members ages 56 years and older said they would be interested in taking online fitness classes. At a significance level of α = 0.05, do the data provide convincing statistical evidence of a difference in the proportion of all exercise center members ages 18 to 55 years who would be interested in taking online fitness classes and the proportion of all exercise center members ages 56 years and older who would be interested in taking online fitness classes? Complete the appropriate inference procedure to justify your response.
Rubric Criteria (4)
q1_method_hypothesesIdentifies a two-sample z-test for a difference in population proportions, defines the proportions in context, and states H0: p1 − p2 = 0 versus Ha: p1 − p2 ≠ 0.
1.0000pts
q1_conditionsChecks random sampling, independence/10% conditions, and the large-count condition using the pooled expected counts 55.25, 114.75, 74.75, and 155.25.
1.0000pts
q1_calculationCorrectly calculates or reports the two-proportion z-statistic and a compatible two-sided p-value, approximately 0.359.
1.0000pts
q1_conclusionCompares the p-value with α = 0.05, makes the correct decision about H0, and concludes in context that the data do not provide convincing evidence of a difference.
1.0000pts
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