FREE SAT Data Analysis & Statistics Questions and Answers 3

Question 1

A study finds that students who eat breakfast have higher test scores than those who don't. Which design would BEST establish that eating breakfast CAUSES higher test scores?

Accepted Answer

A randomized controlled experiment where students are randomly assigned to breakfast or no-breakfast conditions

Answer

A larger observational study with more students

Answer

A survey asking students whether they believe breakfast helps their performance

Answer

Comparing breakfast habits across different schools with different test score averages

Question 2

A survey of 500 adults asks: 'Do you agree that our community should invest more in parks?' 450 (90%) say yes. What is a critical limitation of this data for making policy recommendations?

Accepted Answer

The question wording is leading — 'agree' bias and positive framing likely inflated the 'yes' response

Answer

The sample size of 500 is too small to be meaningful

Answer

Surveys are never valid sources of data for policy decisions

Answer

90% agreement is too high to be statistically possible

Question 3

Which of the following is MOST likely an example of voluntary response bias in a survey?

Accepted Answer

An online poll on a news website where any visitor can choose to respond

Answer

A researcher randomly selects households from a city directory to survey

Answer

A telephone survey using random digit dialing

Answer

A classroom survey where the teacher selects students to respond

Question 4

A study reports that a new drug reduces blood pressure by an average of 8 mmHg in the treatment group, compared to 2 mmHg in the placebo group. The p-value is 0.03. What does this mean?

Accepted Answer

If the drug had no effect, there would be only a 3% chance of observing a difference this large by random chance — suggesting the result is statistically significant

Answer

The drug reduces blood pressure by 3% across all patients

Answer

3% of patients showed improvement with the drug

Answer

The drug is 3 times more effective than the placebo

Question 5

A school district's average SAT score is 1,050. Looking at individual school averages, only 3 of 20 schools have averages above 1,050. What might explain this apparent paradox?

Accepted Answer

Simpson's Paradox or the influence of one or more schools with very large student populations and high scores

Answer

The district average must be incorrectly calculated

Answer

Individual school averages cannot be compared to district averages

Answer

The district average is the median, not the mean, of all schools

Question 6

A researcher compares test scores from two groups: Group A shows a mean of 72 with standard deviation 15; Group B shows a mean of 75 with standard deviation 3. Which group has less variability in scores?

Accepted Answer

Group B (SD=3) shows less variability — scores cluster tightly around the mean

Answer

Group A (SD=15) shows less variability

Answer

Both groups have equal variability since the means are close

Answer

Variability cannot be determined from standard deviation alone