AP Statistics — Practice Exam 1

Total: 55 points · ~1 hour 45 min. Section I: 15 multiple-choice (1 pt). Section II: 1 investigative free-response (40 pts, condensed). Calculator allowed throughout.

Section I — Multiple Choice

1. The median is preferred over the mean as a measure of center when data are (A) skewed or have outliers (B) symmetric (C) categorical (D) normal
2. A z-score of −1.5 means a value is (A) in the 15th percentile (B) negative only (C) 1.5 standard deviations below the mean (D) 1.5 units below the mean
3. In a right-skewed distribution, typically (A) mean = median (B) there is no mode (C) mean < median (D) mean > median
4. The IQR equals (A) Q3 − Q1 (B) max − min (C) mean − median (D) 2 × SD
5. Adding 5 to every value in a data set (A) increases the SD by 5 (B) leaves the SD unchanged (C) doubles the SD (D) makes the SD zero
6. A simple random sample is one in which (A) every group of n individuals is equally likely (B) people are chosen by convenience (C) only volunteers are used (D) the first n people are taken
7. Which is an example of bias? (A) random assignment (B) blinding (C) a large sample (D) a voluntary-response online poll
8. By the empirical rule, ~95% of normal data lie within (A) 2 SD (B) 1 SD (C) 3 SD (D) 0.5 SD of the mean
9. In an experiment, the purpose of a control group is to (A) increase sample size (B) provide a baseline for comparison (C) introduce bias (D) avoid randomization
10. If P(A) = 0.3, P(B) = 0.5, and A and B are independent, then P(A and B) = (A) 0.8 (B) 0.2 (C) 0.15 (D) 0.65
11. A residual is (A) predicted − observed (B) observed − predicted (C) the slope (D) the correlation
12. A correlation of r = −0.9 indicates (A) a strong negative linear relationship (B) a weak positive relationship (C) no relationship (D) causation
13. Increasing the sample size generally (A) increases the variability of the sample mean (B) decreases the standard error (C) biases the estimate (D) has no effect
14. A 95% confidence interval means (A) 95% of the data lie in the interval (B) we are 95% confident the method captures the true parameter (C) the parameter is random 95% of the time (D) the sample is 95% accurate
15. Which method divides the population into groups and samples within each? (A) convenience sampling (B) stratified random sampling (C) a census (D) voluntary response

Section II — Free Response (condensed)

Q1 (~40 pts). A researcher records hours studied (x) and exam score for 8 students and fits a least-squares line: ŷ = 40 + 8x, with r = 0.85.

• (a) Interpret the slope in context. (8)
• (b) Interpret r in context. (6)
• (c) Predict the score for a student who studies 5 hours. (6)
• (d) A student who studied 5 hours actually scored 75. Compute and interpret the residual. (8)
• (e) Does this study show that studying causes higher scores? Explain. (6)
• (f) Describe how you would redesign this as an experiment. (6)

Answer Key (Section I)

FRQ worked solution (Q1)

• (a) For each additional hour studied, the predicted exam score increases by 8 points.
• (b) r = 0.85 → a strong, positive, linear association between hours studied and score.
• (c) ŷ = 40 + 8(5) = 80.
• (d) Residual = observed − predicted = 75 − 80 = −5; the student scored 5 points below the prediction.
• (e) No — the data are observational; lurking variables (e.g. prior ability) could explain the link. Correlation ≠ causation.
• (f) Randomly assign students to study amounts under controlled conditions, then compare scores; random assignment permits a causal conclusion.

AP score guide (approx.)

Section I (15) + Section II (40) = 55 points. Map: 5 ≈ 68%+, 4 ≈ 55–67%, 3 ≈ 40–54%, 2 ≈ 28–39%, 1 ≈ below. Official cut scores vary.