AP Statistics Practice Test 2027

• 2 points: Clear statistical investigative question with population and response.
• 3 points: Valid randomized design; blocking by school is acceptable and must be described correctly.
• 2 points: Correct scope—random assignment supports causation; representative sampling/coverage supports population generalization.
• 2 points: Plausible bias identified and explained in context.
• 1 point: Communication is precise and uses statistical language without overclaiming.

A strong solution blocks by high school, randomly assigns seniors within each school to reminder or control, uses administrative submission status as the response, and distinguishes causal inference from population generalization.

• 2 points: Binomial model with n=100, p=0.18; fixed n, two outcomes, constant p, and approximate independence justified by the random sample being under 10% of the trip population.
• 2 points: μX=18 and σX=√[100(.18)(.82)]≈3.842.
• 2 points: μp̂=.18 and σp̂=√[(.18)(.82)/100]≈.0384.
• 2 points: Large-count condition np=18 and n(1−p)=82 supports approximate Normality.
• 2 points: Correct repeated-sampling interpretation of the standard deviation.

X~Binomial(100,.18), with mean 18 and SD about 3.842. The sampling distribution of p̂ is centered at .18 with SD about .0384 and is approximately Normal because expected successes and failures are both at least 10.

• 2 points: Parameters defined; H0:pA−pB=0 and Ha:pA−pB≠0.
• 2 points: Random/independent samples and large-count conditions checked with pooled proportion.
• 3 points: p̂c=228/360=.6333; SE≈.05080; z≈2.625.
• 1 point: Two-sided p-value≈.0086.
• 2 points: Reject H0 at .05; convincing evidence that the population proportions differ.

p̂A=.700, p̂B=.5667, difference=.1333. With pooled p̂=.6333, SE≈.05080 and z≈2.625, the two-sided p-value is about .0087, so reject H0 and conclude the population proportions differ.

• 2 points: Correct population parameters and a valid inference condition such as independent/random observations with large-count requirements.
• 2 points: p̂new=124/200=0.620, p̂standard=96/180≈0.533, difference≈0.087, interpreted as about 8.7 percentage points higher in the sample.
• 2 points: Correct 95% confidence-interval interpretation for the population difference and evidence of a positive difference because 0 is excluded.
• 2 points: ŷ=8.4+2.6(7)=26.6 minutes; residual=29−26.6=2.4 minutes.
• 2 points: Residual plot supports linear form over the observed range; causal claims require an appropriate randomized design, not regression association alone.

The sample difference is about 0.087. The 95% interval from 0.012 to 0.161 supports a higher population on-time rate for the new system. For a 7-mile route, predicted travel time is 26.6 minutes and the residual is +2.4 minutes. A patternless residual plot supports the linear form for similar trips, but association in regression does not by itself establish causation.