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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: AP Statistics Unit 1 (2026-27) · Level: Grade 12 AP Statistics
Question 1 Statistical Questions (2 points)
(a) Prices vary between stores, so variability is expected: statistical. (b) There is one height: not statistical.
(a) statistical; (b) not statistical
Scoring: 1 point each part, with a reason about variability.
Question 2 Simple Random Sample Selection (3 points)
(a) Reading left to right: 893, 104, 167, 692, 861, 834, 085, 543. Valid, new labels are 104, 167, 085, 543. (b) Groups above 600 (such as 893) or equal to 000 are skipped, and a repeated label is skipped. (c) Every student has the same chance, and every group of 4 students is equally likely to be the selected group.
Students 104, 167, 085, 543
Scoring: 1 point for each part: correct four labels, correct handling of invalid and repeated groups, explanation of equal chance for every group.
Question 3 Identify the Sampling Method (2 points)
(a) Whole groups are randomly chosen: a cluster sample. (b) A stratified sample takes some individuals from every group; a cluster sample takes all individuals from only some groups.
(a) cluster sample
Scoring: 1 point each part.
Question 4 Types of Bias (2 points)
(a) Undercoverage: households without landlines cannot be selected. (b) Nonresponse: many chosen households did not answer, and they may differ from those who did.
(a) undercoverage; (b) nonresponse
Scoring: 1 point each part.
Question 5 Observation and Confounding (2 points)
(a) No: participants chose their own treatment, so it is an observational study. (b) People who choose to take vitamins may also eat better or sleep more, and those habits could explain fewer colds.
Observational; possible confounder: healthy habits
Scoring: 1 point each part.
Question 6 Design a Randomized Experiment (3 points)
Number the customers 01 to 30 and use a random number generator to select 15 for the new recipe; the others taste the current recipe. Both samples look identical and customers are not told which recipe they have (blinding), so expectations do not affect ratings. Compare the distributions of ratings in the two groups (for example, with the mean).
Randomly assign 15 customers to each recipe, blind them, compare ratings
Scoring: 1 point random assignment described, 1 point blinding or other bias control, 1 point comparison of the groups.
Question 7 Placebo and Blinding (2 points)
(a) It is a placebo. It gives both groups the experience of taking a pill so that expectations are balanced. (b) Neither the participants nor the people measuring the response know who is in which group.
(a) placebo; (b) participants and evaluators are both unaware of the treatment
Scoring: 1 point each part.
Question 8 Matched Pairs (2 points)
(a) A matched-pairs design (each runner is a block with two measurements). (b) If everyone used shoe A first, fatigue or learning could be confounded with the shoe brand; randomizing the order balances such effects.
(a) matched pairs; (b) balances order effects
Scoring: 1 point each part.
Question 9 Scope of Inference (2 points)
(a) Yes. Random assignment supports a cause-and-effect conclusion. (b) The sample was randomly selected from the district’s teenagers, so the results can be generalized to all teenagers in that district.
(a) yes, cause and effect; (b) all teenagers in the district
Scoring: 1 point each part with justification.
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