These Digital SAT questions describe a study or survey and ask whether its conclusion can be generalized to a population, whether it supports cause-and-effect, or whether the design has a flaw.
Two different design choices answer two different questions. Random sampling — randomly choosing who is measured — determines whether results can be generalized to a population. Random assignment — randomly placing participants into groups (treatment vs. control) — determines whether you can conclude causation. A study can have either, both, or neither.
Use Sample vs. Assignment vs. Claim: identify whether the study used random sampling, identify whether it used random assignment, then check whether the stated claim matches what that combination actually supports.
Researchers randomly selected 500 people from a city, then simply asked whether they exercise regularly and measured their stress level — no groups were assigned. They found that people who exercise regularly reported lower stress. Walk through evaluating that claim below.
A study finds that city residents who own a gym membership have lower average blood pressure than those who don't. Which statement is best supported?
These two ideas get tested against each other constantly, so keep them separate by what question each one answers. Random sampling answers: “Can I trust this result applies to the population I sampled from?” Random assignment answers: “Can I trust that the treatment — not something else — caused the difference I observed?” A well-designed experiment often uses both.
Classify the design used in each scenario.
A company wants to know if a new packaging design increases sales. It randomly assigns 40 of its 80 stores to use the new packaging and the other 40 to keep the old packaging, then compares sales. What does the random assignment allow them to conclude if sales are higher in the new-packaging stores?
Two variables can move together without one causing the other. Classic example: ice cream sales and drowning incidents both rise in the summer — not because ice cream causes drowning, but because a third factor (warm weather, more swimming) drives both. This is called a confounding variable.
When the SAT describes an observational study (no random assignment) and asks what can be concluded, the safe answer is almost always “an association, not a cause” — unless a confounding explanation is even more directly suggested by the choices.
A researcher notices that in a large dataset, towns with more libraries tend to have lower crime rates. Which of the following is the most likely explanation, other than libraries directly reducing crime?
A handful of flaws show up again and again: a nonrandom or self-selected sample (only people who chose to respond), no control group to compare against, and results from one group applied to a different group that wasn't part of the study. When you see a strong claim (“X causes Y” or “X% of everyone believes...”), check the study design before accepting it.
A magazine surveys its own readers online and reports that “80% of Americans prefer Brand X.” What is the main flaw in this claim?
These mix sampling vs. assignment, spotting confounding variables, and identifying weak survey designs — the recurring themes across this question type.
A poll only surveys people leaving a gym about exercise habits. What kind of bias does this introduce?
True or false: random assignment allows researchers to conclude causation.
A study observes (does not assign) that students who eat breakfast have higher grades. What can be concluded?
A drug trial randomly assigns patients to a drug group or a placebo group. What does this support?
A national survey uses a random sample of 1,500 adults across all 50 states. What does this support?
Two variables rise together because both are caused by a third variable. What is this called?
Once you can spot sampling and assignment reliably, you're ready to combine this with margin of error, which quantifies exactly how much uncertainty a sample's estimate carries.
Here are five practice problems that help you hone your skills. Use the same method we learned earlier above to solve these problems. Remember, practice makes perfect.
A university randomly selects 600 students from its full enrollment to survey about dining hall satisfaction. What does the random sampling most directly support?
Researchers randomly assign volunteers to either take a new supplement or a placebo for 8 weeks, then compare energy levels. What does the random assignment support?
A news article states that “coffee drinkers live longer, so drinking coffee causes a longer life.” What is the flaw in this claim?
A city's park department wants feedback and posts a survey link only on its own social media page, which is followed mostly by frequent park users. What kind of bias does this introduce?
A study randomly samples patients from a hospital's full patient population and randomly assigns them to two treatments, then compares outcomes. If Treatment A shows better outcomes, what can be concluded?
Related: Data inference & margin of error · Distributions, center & spread · Two-variable data & scatterplots · SAT Math overview