Bluebook SAT Test Data Analysis & Statistics 4

Question 1

The line of best fit for a scatterplot of hours studied (x) versus exam score (y) is ŷ = 4.2x + 55. A student who studied 8 hours received a score of 87. What is the residual for this data point, and what does it indicate about the model's prediction?

Accepted Answer

−1.6; the student performed below the model's prediction

Answer

The predicted score is ŷ = 4.2(8) + 55 = 33.6 + 55 = 88.6. The residual = actual − predicted = 87 − 88.6 = −1.6. A negative residual means the actual score fell below the model's prediction — the line overestimates this student's score, not underestimates it. Choice C reverses the interpretation of a negative residual.

Question 2

Dataset X has a mean of 50 and a standard deviation of 2. Dataset Y has a mean of 200 and a standard deviation of 8. Which statement correctly compares the relative variability of the two datasets?

Accepted Answer

Both datasets have equal relative variability

Answer

Relative variability is measured by the coefficient of variation (CV = standard deviation ÷ mean). For Dataset X: CV = 2/50 = 0.04 (4%). For Dataset Y: CV = 8/200 = 0.04 (4%). Despite Dataset Y having a larger absolute standard deviation, both datasets spread by the same proportion relative to their respective means. Comparing raw standard deviations across different scales is misleading.

Question 3

A poll of 400 likely voters finds that 52% support Candidate A, with a margin of error of ±4 percentage points at the 95% confidence level. A news anchor declares: 'This poll proves Candidate A will win.' Which of the following best identifies the flaw in this claim?

Accepted Answer

The confidence interval includes values below 50%, so a majority may not actually support Candidate A

Answer

The 95% confidence interval is 52% ± 4%, which spans from 48% to 56%. Because this interval includes values below 50%, it is statistically possible that fewer than half of all likely voters support Candidate A. The anchor's error is treating the point estimate (52%) as a certainty rather than recognizing the range of plausible true values the interval represents.

Question 4

A streaming service surveys 500 users who watched at least one documentary in the past 30 days and finds that 78% of them prefer documentaries over other genres. The service concludes that 78% of all subscribers prefer documentaries. Which of the following best explains the primary flaw in this conclusion?

Accepted Answer

The sampling method systematically overrepresents users who already watch documentaries

Answer

This is a classic example of sampling bias. By restricting the survey to users who already watched a documentary, the service excluded the portion of subscribers who never watch documentaries — likely the group least inclined to prefer them. The sample is not representative of all subscribers, so the 78% figure cannot be generalized to the full population. Sample size (choice A) is irrelevant when the selection process is fundamentally biased.

Question 5

A hospital compares two drugs across two independent trials. Drug A cured 80% of patients in Trial 1 and 75% in Trial 2. Drug B cured 70% of patients in Trial 1 and 65% in Trial 2. A researcher concludes Drug A is more effective overall. Which piece of additional information would most directly challenge this conclusion?

Accepted Answer

Whether Drug A treated far more patients in the lower-cure-rate trial while Drug B treated far more patients in the higher-cure-rate trial

Answer

This scenario describes Simpson's Paradox. Even though Drug A outperforms Drug B within each individual trial, the overall combined cure rate can reverse if the patient counts are unequal across trials. If Drug A treated mostly patients in Trial 2 (the harder trial, lower cure rates) while Drug B treated mostly patients in Trial 1 (the easier trial, higher cure rates), Drug B's overall weighted average could equal or exceed Drug A's. The within-group advantage does not guarantee an overall advantage when group sizes differ substantially.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Data Analysis & Statistics 4