AP Statistics — Practice Exam 3
Format: Section I — 18 multiple-choice questions · Section II — 1 investigative FRQ Suggested time: 35 min (MCQ) + 20 min (FRQ) · calculator permitted · computations verified. (Answers spread A–D.)
Section I — Multiple Choice
1. A summary value computed from a sample is a: A) parameter B) statistic C) census D) variable
2. Which measure of center resists outliers? A) mean B) range C) median D) standard deviation
3. The standard deviation measures: A) center B) shape C) spread D) outliers only
4. For 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)
5. The complement rule states P(not A) = A) 1 − P(A) B) P(A) − 1 C) 1/P(A) D) P(A)²
6. The expected value of a random variable is its long-run: A) mode B) mean C) range D) maximum
7. By the Central Limit Theorem, as n grows the sampling distribution of x̄ becomes more: A) skewed B) uniform C) normal D) bimodal
8. The standard error of the sample mean is: A) σ B) σ·n C) s² D) σ/√n
9. A 95% confidence level means the method captures the parameter in: A) 95% of repeated samples B) 95% of the data C) exactly this sample D) no samples
10. The margin of error equals the critical value times the: A) sample size B) mean C) standard error D) median
11. A small p-value (below α) leads you to: A) fail to reject H₀ B) reject H₀ C) accept H₀ D) take no action
12. A Type I error is: A) failing to reject a false H₀ B) accepting a true H₀ C) rejecting a true H₀ D) a correct decision
13. Inference about a population mean (σ unknown) uses the: A) z-distribution B) t-distribution C) chi-square D) F-distribution
14. df for a one-sample t-test with n = 16 is: A) 14 B) 15 C) 16 D) 17
15. The chi-square statistic is computed as Σ: A) (O−E)/E B) (O−E)²/E C) (O−E)² D) O/E
16. A residual equals: A) predicted − observed B) slope × x C) observed − predicted D) r²
17. If r = 0.7, then r² = A) 0.7 B) 0.49 C) 0.35 D) 0.84
18. Increasing the sample size generally: A) increases variability B) introduces bias C) decreases the standard error D) changes the mean
Section II — Investigative FRQ (4 points)
A company tests whether a new training cuts task-completion time. It randomly assigns 50 workers to training and 50 to a control group, then compares mean times. (a) Identify the explanatory and response variables. (1 pt) (b) Explain why random assignment matters here. (1 pt) (c) State appropriate null and alternative hypotheses. (1 pt) (d) If p = 0.01 at α = 0.05, state the conclusion in context. (1 pt)
Answer key (Section I)
| Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|
| 1 | B | 7 | C | 13 | B |
| 2 | C | 8 | D | 14 | B |
| 3 | C | 9 | A | 15 | B |
| 4 | D | 10 | C | 16 | C |
| 5 | A | 11 | B | 17 | B |
| 6 | B | 12 | C | 18 | C |
Key distribution: A×2, B×7, C×8, D×1.
Reasoning (Section I)
1. (B) A sample summary is a statistic. 2. (C) The median resists outliers. 3. (C) SD measures spread. 4. (D) Multiply for independent events. 5. (A) P(not A) = 1 − P(A). 6. (B) Expected value is the long-run mean. 7. (C) CLT: larger n → more normal. 8. (D) SE = σ/√n. 9. (A) Confidence = long-run capture rate. 10. (C) ME = critical value × SE. 11. (B) p < α → reject H₀. 12. (C) Type I = rejecting a true null. 13. (B) Unknown σ → t. 14. (B) df = n − 1 = 15. 15. (B) χ² = Σ(O−E)²/E. 16. (C) Residual = observed − predicted. 17. (B) 0.7² = 0.49. 18. (C) Larger n → smaller SE.
FRQ rubric (4 pts)
- (a) (1) Explanatory = training (training vs control); response = task-completion time.
- (b) (1) Random assignment balances confounders, allowing a cause-and-effect conclusion.
- (c) (1) H₀: μ_train = μ_control; Hₐ: μ_train < μ_control (training reduces time).
- (d) (1) Since 0.01 < 0.05, reject H₀; there is convincing evidence the training reduces mean completion time.
Pedagogy: inference conclusions must be in context — tie "reject H₀" to the real claim about completion time.