AP Statistics practice questions and exam guide

If A and B are MUTUALLY EXCLUSIVE with P(A) = 0.3, P(B) = 0.5, then P(A or B) =

1. 0.15
2. 0.50
3. 0.80
4. 0.30

Answer: C — 0.80

Mutually exclusive: P(A or B) = P(A) + P(B) = 0.3 + 0.5 = 0.80. (A) Multiplies — but ME events have P(A and B) = 0. (B), (D) Single probabilities.

For a binomial setting, when is the sampling distribution of p̂ approximately normal?

1. Always
2. When np ≥ 10 AND n(1−p) ≥ 10 (large-counts condition)
3. When n < 30
4. Never

Answer: B — When np ≥ 10 AND n(1−p) ≥ 10 (large-counts condition)

Large counts: np ≥ 10 and n(1−p) ≥ 10. Then p̂ ~ approximately N(p, √(p(1−p)/n)). For inference, use p̂ in place of p when conditions met. CLT-justified.

If the P-value for the slope is 0.001 in a regression with α = 0.05, what is your conclusion?

1. Reject H₀: there is sufficient evidence that the true slope is NOT zero — i.e., there IS a linear relationship between the variables
2. Fail to reject H₀
3. Accept the null
4. The slope is 0.001

Answer: A — Reject H₀: there is sufficient evidence that the true slope is NOT zero — i.e., there IS a linear relationship between the variables

H₀: β = 0 (no linear relationship). H_a: β ≠ 0 (linear relationship exists). P = 0.001 < α = 0.05 → reject H₀. Conclude: sufficient evidence of a linear relationship. Always interpret in context: 'The data provide strong evidence of a linear association between X and Y.'

Stratified random sampling improves inference by:

1. Dividing the population into homogeneous strata and sampling within each, reducing variability of estimates
2. Sampling only one stratum
3. Eliminating the need for randomization
4. Increasing bias

Answer: A — Dividing the population into homogeneous strata and sampling within each, reducing variability of estimates

A) Definition + benefit. B/C/D) Each misstates the design.

An observational study finds people who eat broccoli often have lower cancer rates. The headline 'Broccoli prevents cancer' is misleading because:

1. Broccoli intake is not measured precisely
2. Cancer rates can't be measured
3. Sample size was too large
4. Confounding variables (e.g., overall healthy lifestyle) may explain both broccoli consumption and lower cancer rates

Answer: D — Confounding variables (e.g., overall healthy lifestyle) may explain both broccoli consumption and lower cancer rates

Observational → causal claims unwarranted due to confounders. Healthier overall lifestyle could drive both. (A) Possible but not the main issue. (C), (B) Unjustified.

X and Y are independent random variables with σX = 3 and σY = 4. The standard deviation of X − Y is:

1. 1
2. 7
3. 5
4. 25

Answer: C — 5

Variances ADD even for differences: σ²(X−Y) = σ²X + σ²Y = 9 + 16 = 25 → σ = 5. (A) Subtracts SDs. (B) Adds SDs. (D) Forgets square root.

A dataset of test scores has Q1 = 70, Q3 = 86. According to the 1.5·IQR rule, a score is a low outlier if it is below:

1. 70 − 16 = 54
2. 70 − 8 = 62
3. 70 − 24 = 46
4. 70 − 32 = 38

Answer: C — 70 − 24 = 46

IQR = 86 − 70 = 16. Fences: Q1 − 1.5·IQR = 70 − 24 = 46. (A) subtracts the IQR itself, not 1.5·IQR. (B) uses 0.5·IQR. (D) uses 2·IQR. AP rubric: 1.5·IQR exactly.

A dataset is strongly RIGHT-SKEWED. Which is true about its mean and median?

1. Mean = median
2. Mean > median (a few high values pull the mean up)
3. Mean < median
4. Cannot be determined

Answer: B — Mean > median (a few high values pull the mean up)

Right-skewed (positive skew) distributions have a long right tail with high outliers. The mean is pulled toward the tail (higher); median is more resistant. For left-skewed: mean < median. For symmetric/normal: mean ≈ median.

A study reports r = 0.85 between hours studied and test score. The MOST appropriate interpretation is:

1. Hours of studying CAUSE higher test scores
2. There is no relationship
3. There is a strong positive linear association — but correlation alone does not prove causation
4. The relationship is exactly linear with no error

Answer: C — There is a strong positive linear association — but correlation alone does not prove causation

C) Correlation ≠ causation; strong positive association noted. A/B/D) Each over- or under-states.

In a least-squares regression ŷ = b₀ + b₁x, the slope b₁ represents:

1. The y-intercept
2. The standard deviation
3. The correlation
4. The PREDICTED change in y for a one-unit increase in x (in context, with appropriate units)

Answer: D — The PREDICTED change in y for a one-unit increase in x (in context, with appropriate units)

Slope = predicted Δy per unit Δx. Interpretation must reference the specific variables and units (e.g., 'For each additional inch of height, predicted weight increases by 5 pounds'). AP rubric demands contextual language.

In a regression of y on x with r = −0.7, sy = 14, and sx = 2, the slope is:

1. −0.1
2. −0.7
3. −4.9
4. −9.8

Answer: C — −4.9

b = r · (sy/sx) = −0.7 · (14/2) = −0.7 · 7 = −4.9. (A) divides instead of multiplies. (B) uses r alone. (D) doubles the result by mistake.

A study finds the difference between two treatments has p-value 0.001 with large n. Which is true?

1. The difference is practically large
2. The result is not generalizable
3. The treatment causes the outcome
4. The difference is statistically SIGNIFICANT, but may not be practically important — large n can detect tiny effects

Answer: D — The difference is statistically SIGNIFICANT, but may not be practically important — large n can detect tiny effects

Statistical significance ≠ practical importance. Large n shrinks SE, so small effects yield small p-values. Effect SIZE (Cohen's d, % difference, etc.) must accompany p-value. AP exam emphasizes this distinction repeatedly.

Expected count for cell in two-way table?

E = (row total × column total) / grand total.

Common interpretation error: 'rejected H₀ proves Hₐ'?

Inference is probabilistic — doesn't 'prove' anything. We have evidence; future research can refine.

What's an SRS — random sampling key feature?

Every sample of size n has an equal chance — eliminates selection bias.

Why is replication needed in experiments?

Reduces effect of chance variation; supports reliable conclusions.

What is an influential point?

A point that, when removed, substantially changes the regression line. Often outliers in x.

Sample size for desired ME?

n = (z*/ME)² · p̂(1−p̂). Use 0.5 if no estimate of p (most conservative).