1. A study finds that cities with more hospitals have higher death rates. Which statement is most accurate?

• Hospitals cause deaths — people should avoid them.
• This is likely a correlation explained by confounding: sicker people go to cities with more hospitals.
• This proves hospitals are ineffective.
• The correlation is too strong to be coincidental — causation is confirmed.

2. Which of the following correctly defines a confounding variable?

• A variable that has no relationship to the study.
• A third variable that influences both the independent and dependent variables, making correlation appear causal.
• A variable that proves causation between two correlated variables.
• A variable that removes bias from a study.

3. Consider: I. Two variables can be strongly correlated without one causing the other. II. Establishing causation requires a randomized controlled experiment. III. A correlation coefficient of +0.95 proves causation.

• I only
• I and II only
• I, II, and III
• II and III only

4. Research shows that people who own umbrellas get wet less often. The most accurate conclusion is:

• Owning an umbrella causes people to get wet less often (causation).
• Getting wet less often causes people to buy umbrellas.
• There is a correlation, likely because umbrella owners use them on rainy days.
• The data is invalid because correlation is too obvious.

5. A researcher wants to determine if a new drug lowers blood pressure. Which study design establishes causation?

• Survey patients who take the drug and ask if their pressure improved.
• Randomly assign patients to drug or placebo groups and compare results.
• Compare blood pressure of drug-takers vs. non-drug-takers without random assignment.
• Find 10,000 cases of patients who improved while taking the drug.

6. Shoe size and reading ability are positively correlated in a sample of school children. The most likely explanation is:

• Reading improves physical development, increasing shoe size.
• Children with large feet are naturally better readers.
• Age is a confounding variable: older children have larger feet and better reading skills.
• The study contains errors because this correlation is impossible.

7. A data analyst observes that ice cream sales and sunburn cases rise together every summer. She concludes that ice cream causes sunburns. What is wrong with her reasoning?

• Ice cream and sunburns are not actually correlated.
• Hot weather is a confounding variable that causes both, and correlation does not imply causation.
• The correlation is too weak to draw any conclusions.
• Sunburns cause ice cream cravings, not the reverse.

8. Which question can be answered by observational data (correlation) alone?

• Does studying more CAUSE higher test scores?
• Do students who study more get higher test scores on average?
• Would making students study more improve their test scores?
• Is studying the reason some students outperform others?

9. A medical study of 500,000 people finds that coffee drinkers have lower rates of a certain disease. This finding:

• Proves that coffee prevents the disease.
• Suggests a correlation that warrants further investigation, but does not establish causation.
• Is invalid because 500,000 is not a large enough sample.
• Proves causation because the sample size is very large.

10. A newspaper reports: “Students who play video games score lower on math tests.” Which is the strongest alternative explanation?

• Video games directly impair mathematical reasoning.
• Students who play many hours of video games have less time to study, and less study time causes lower scores.
• The study was conducted incorrectly.
• Low math scores cause students to seek entertainment in video games.