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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: AP Statistics Unit 4 (2026-27) · Level: Grade 12 AP Statistics
Question 1 Margin of Error (2 points)
SE = 7.5/√20 = 1.677. df = 19, t* = 2.093. ME = 2.093 × 1.677 = 3.51.
SE ≈ 1.68; ME ≈ 3.51 miles
Scoring: 1 point for SE, 1 point for t* and margin of error.
Question 2 One-Sample t Interval (3 points)
(a) Random sample; the harvest is much larger than 120 tomatoes; the dotplot is roughly symmetric with no outliers. (b) df = 11, t* = 2.201, SE = 1.462, ME = 3.22: (123.78, 130.22). (c) We are 95% confident that the mean weight of all tomatoes in the harvest is between 123.8 and 130.2 grams.
(123.8, 130.2) grams
Scoring: 1 point each part.
Question 3 One-Sample t Test (3 points)
t = (48.3 − 50)/(6.2/√25) = −1.371, df = 24, p-value = 0.0915. Since 0.0915 > 0.05, we fail to reject H0: there is not convincing evidence that the mean protein content is less than 50 grams.
t ≈ −1.37, p-value ≈ 0.092; fail to reject H0
Scoring: 1 point for t, 1 point for the p-value, 1 point for the conclusion in context.
Question 4 Paired or Independent (2 points)
(a) Option 1 is paired because each athlete is measured twice. (b) Option 1: a paired t procedure (one-sample t on the differences). Option 2: a two-sample t procedure for independent samples.
Option 1: paired t; Option 2: two-sample t
Scoring: 1 point each part.
Question 5 Paired t Test from Summary (3 points)
t = 2.8/(4.1/√15) = 2.645, df = 14, p-value = 0.0096. Since 0.0096 < 0.05, reject H0: there is convincing evidence that the mean time decreased after training.
t ≈ 2.64, p-value ≈ 0.0096; reject H0
Scoring: 1 point for the statistic, 1 point for the p-value, 1 point for the conclusion.
Question 6 Two-Sample t Test (3 points)
(a) Independent random samples; both boxplots are roughly symmetric without outliers, and each n is about 30. (b) SE = √(9.62/30 + 11.22/28) = 2.748; t = (82.4 − 77.1)/2.748 = 1.929. (c) Since 0.059 > 0.05, fail to reject H0: not convincing evidence that the mean scores differ.
SE ≈ 2.75, t ≈ 1.93; fail to reject H0
Scoring: 1 point each part.
Question 7 Using an Interval (2 points)
(a) Yes: the interval contains only positive values and does not include 0. (b) We are 95% confident that the mean weight loss with Plan A is between 0.6 and 3.4 pounds greater than with Plan B.
Yes; 0 is not in the interval
Scoring: 1 point each part.
Question 8 Choosing a Procedure (2 points)
(a) One-sample t interval for a mean; check that the sample is random and that the data show no strong skew (or n ≥ 30). (b) Two-sample z procedure for a difference of proportions; check that all counts of successes and failures are at least 10.
(a) one-sample t; (b) two-proportion z
Scoring: 1 point each part with a valid condition.
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