SAT Math: Study Design, Sampling, and Causation Practice Questions
Distinguish random sampling from random assignment, identify confounding, and match conclusions to the population and study design. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
Answer the questions below — you get instant feedback and a full explanation for each.
1. Students volunteer for a study and are randomly assigned to use a new study method or their usual method. Which feature most directly supports a causal comparison between the two methods?
Explanation. Random assignment distributes preexisting characteristics between treatment groups by chance, supporting a causal comparison. Volunteering concerns participation and generalizability; using the same test helps measurement but does not itself create comparable treatment groups.
2. An observational survey finds that students who sleep longer tend to earn higher grades. Which conclusion is supported by the design alone?
Explanation. An observational survey can show an association. It does not randomly assign sleep duration, so other factors could explain the pattern. An overall tendency also does not imply the same result for every individual.
3. A town randomly samples 500 registered adult residents from its complete list of registered adult residents. Which population is most directly represented by this sample?
Explanation. The sampling frame is the complete list of registered adult residents in this town. Random sampling supports inference to that population, subject to the study's assumptions; it does not directly represent children, visitors, or adults elsewhere.
4. Researchers randomly assign 60 volunteers from one school to two tutoring methods. What most limits extending the result to all students in the country?
Explanation. Random assignment helps compare the methods among participants. Broad generalization also depends on how participants represent the target population. Volunteers from one school are not a random sample of all students in the country.
5. A town finds that ice cream sales and swimming visits rise together. Which factor is a plausible confounding variable?
Explanation. Warmer weather can increase both demand for ice cream and swimming visits. Temperature can therefore create an association between the two measures without either one causing the other.
6. A researcher posts an optional online poll on a running club's website to estimate exercise habits of all adults in a city. What is the clearest concern?
Explanation. The poll depends on visiting a running website and volunteering a response. Those adults may exercise differently from other city residents. Increasing responses from the same selection process does not by itself remove this selection bias.
📘 Looking for more study material? Browse SAT prep books and study resources. Some links are affiliate links; we may earn a commission at no cost to you.
FAQ
What does random sampling help with?
Random sampling helps a sample represent the population from which it was selected, supporting population estimates under the study's conditions.
What does random assignment help with?
Random assignment helps make treatment groups comparable before treatment and supports causal comparisons. It serves a different purpose from selecting a representative sample.