AP Statistics — Practice Exam 2

Format: Section I — 18 multiple-choice questions · Section II — 1 investigative free-response question Suggested time: 35 min (MCQ) + 20 min (FRQ) · calculator permitted Coverage: Exploring Data · Sampling & Experiments · Probability & Random Variables · Sampling Distributions · Inference. All computations verified. (Correct answers are spread across A–D by design.)

Section I — Multiple Choice

1. A numerical summary computed from a sample is called a: A) parameter B) statistic C) census D) variable

2. Which measure of center is most resistant to outliers? A) mean B) range C) mode D) median

3. In a right-skewed distribution, the mean is usually: A) greater than the median B) less than the median C) equal to the median D) zero

4. The interquartile range (IQR) is equal to: A) max − min B) mean − median C) Q3 − Q1 D) Q1 + Q3

5. The standard deviation is a measure of: A) center B) spread C) shape D) outliers only

6. For two independent events, P(A and B) = A) P(A) + P(B) B) P(A) − P(B) C) P(A) / P(B) D) P(A) · P(B)

7. The complement rule states that P(not A) = A) 1 − P(A) B) P(A) − 1 C) 1 / P(A) D) P(A)²

8. The expected value of a random variable is its: A) mode B) median C) long-run mean D) range

9. By the Central Limit Theorem, as sample size increases the sampling distribution of x̄ becomes more: A) skewed B) normal C) uniform D) bimodal

10. The standard deviation of the sample mean (standard error) is: A) σ B) σ · n C) s² D) σ / √n

11. A "95% confidence level" means that: A) the method captures the true parameter in 95% of repeated samples B) 95% of the data lie in the interval C) the parameter equals 0.95 D) the sample is 95% complete

12. The margin of error equals the critical value multiplied by the: A) sample size B) mean C) standard error D) median

13. A small p-value (below α) leads you to: A) fail to reject the null hypothesis B) reject the null hypothesis C) accept the null hypothesis D) take no action

14. A Type I error occurs when you: A) fail to reject a false null hypothesis B) accept a true null hypothesis C) make a correct decision D) reject a true null hypothesis

15. The correlation coefficient r can take values: A) from −1 to 1 B) from 0 to 1 C) from 0 to 100 D) from −∞ to ∞

16. If r² = 0.64, then |r| = A) 0.40 B) 0.32 C) 0.80 D) 0.64

17. A residual is calculated as: A) predicted − observed B) observed − predicted C) slope × x D) r²

18. Increasing the sample size generally: A) increases variability B) introduces bias C) changes the mean D) decreases the standard error

Section II — Free Response (Investigative Task, 4 points)

A researcher wants to know whether a new study app raises test scores. She randomly assigns 60 students to use the app and 60 to a control group, then compares mean scores. (a) Identify the explanatory and response variables. (1 pt) (b) Explain why random assignment is important here. (1 pt) (c) State appropriate null and alternative hypotheses for comparing the two group means. (1 pt) (d) If the resulting p-value is 0.02 at α = 0.05, state the conclusion in context. (1 pt)

Answer key (Section I)

Key distribution: A×4, B×5, C×4, D×5.

Reasoning (Section I)

1. (B) A sample summary is a statistic; a population summary is a parameter. 2. (D) The median resists outliers; the mean does not. 3. (A) A right tail pulls the mean above the median. 4. (C) IQR = Q3 − Q1. 5. (B) Standard deviation measures spread. 6. (D) Independent events: multiply probabilities. 7. (A) Complement: 1 − P(A). 8. (C) Expected value is the long-run mean. 9. (B) CLT: larger n → more normal sampling distribution. 10. (D) Standard error of the mean = σ/√n. 11. (A) Confidence refers to the long-run capture rate of the method. 12. (C) Margin of error = critical value × standard error. 13. (B) p < α → reject the null. 14. (D) Type I error = rejecting a true null (false positive). 15. (A) −1 ≤ r ≤ 1. 16. (C) |r| = √0.64 = 0.80. 17. (B) Residual = observed − predicted. 18. (D) Larger n reduces the standard error (σ/√n).

FRQ rubric (4 pts)

• (a) (1) Explanatory = app use (app vs control); response = test score.
• (b) (1) Random assignment balances confounding variables across groups, allowing a cause-and-effect conclusion.
• (c) (1) H₀: μ_app = μ_control (no difference); Hₐ: μ_app > μ_control (app group scores higher).
• (d) (1) Since 0.02 < 0.05, reject H₀; there is convincing evidence the app raises mean test scores.

Pedagogy: inference answers must be in context — "reject H₀" alone is incomplete; "there is convincing evidence the app raises mean scores" earns the point. Always tie the statistical decision back to the real-world claim.