Math · Problem-Solving and Data Analysis

Evaluating Statistical Claims on the Digital SAT

These questions hand you a study and ask what conclusion it actually supports. No arithmetic, no formulas: just a description of how data was collected and four sentences, three of which claim more than the study can back up. If you know two design rules, you can usually spot the right answer quickly.

Rule one: random sampling controls who the results apply to. A random sample from a city lets you generalize to that city, and a self-selected sample (call-in polls, online surveys people choose to take) lets you generalize to nobody. Rule two: random assignment controls what you can say about cause. If researchers did not randomly assign people to treatments, the study can show an association but never that one thing caused another.

Like the other statistics skills, this one is low-volume on the test but nearly pure logic. Students who have never seen the format burn a minute rereading and still guess; students who have seen it check two design questions and move on. That is a cheap point either way, and it should be yours.

New to the Digital SAT? Start with how the test is structured and scored.

What the SAT actually tests

Random sampling versus random assignment: sampling determines which population the results generalize to; assignment determines whether a cause-and-effect conclusion is justified.
Spotting biased or self-selected samples (call-in polls, volunteer online surveys) and recognizing that no percentage from them, however large the sample, describes the full population.
Matching conclusions to the sampled population: a random sample of one school supports claims about that school only.
Observational studies versus experiments: measuring existing behavior supports association; only an experiment with random assignment supports causation.
Recognizing the strongest supportable conclusion, which is usually a modest one: an association exists in the sampled population, and nothing more.
Understanding that a larger sample reduces uncertainty but cannot fix a flawed collection method.

Strategies that work

Ask the two design questions

For every study, check: were participants randomly SELECTED, and were they randomly ASSIGNED to groups? Random selection lets conclusions generalize to the sampled population. Random assignment lets conclusions claim cause and effect. Each answer choice lives or dies on those two checks.

Downgrade causal language

If people chose their own behavior (meditating, exercising, eating breakfast), the study is observational and can only show an association. Cross out any choice with "causes," "improves," "leads to," or "results in" unless the study randomly assigned the treatment.

Trace the sample back to its population

Write down exactly who was sampled and how. The correct conclusion mentions that group and no larger one. A choice that expands from "adults in the city" to "all adults" is wrong even if everything else in it is fine.

Prefer the most modest true statement

When two choices survive the design checks, the correct one is almost always the weaker claim: "an association exists in this population" beats anything with certainty or cause. The SAT rewards knowing the limits of data, not enthusiasm about it.

Mistakes to avoid

Inferring causation from an observational study. People who meditate having lower blood pressure does not mean meditation lowers blood pressure; the groups may differ in many other ways.
Generalizing from a self-selected sample. Two thousand call-in responses still only describe people who chose to call.
Fixing the wrong flaw: saying a biased sample is "too small" when the real problem is that it was not randomly selected. Size and randomness are separate issues.
Naming the wrong kind of bias. A voluntary-response sample (people opt in, like a call-in poll) and a convenience sample (whoever is easiest to reach, like the first shoppers at one store) are both non-random, but the SAT wants the one that actually matches the study. Pick the mechanism the scenario describes.
Extending conclusions past the sampled population, like turning a one-city sample into a national claim.
Overcorrecting into "no conclusion is possible." A well-run random sample does support a conclusion; it is just a modest one about association within that population.
Treating a sample percentage as exact. A random sample gives an estimate with a range, not a precise population value, and two random samples will not match exactly. On "must be true" questions, the safe statement is the plausible range, not a single number.

Practice with Nova, your Math coach

Answer right here and Nova walks you through it, just like in a drill. Difficulty labels are relative within this skill.

Tip: the Calculator button on each question opens the same Desmos graphing calculator you get on the real Digital SAT. Try solving these with it.

Question 1Easy

A radio host invited listeners to call the station and share whether they supported a proposed teen curfew in their city. Of the 2,000 listeners who called, 78% said they opposed the curfew.

Which of the following is the best reason the results should NOT be used to conclude that about 78% of the city's residents oppose the curfew?

Pick an answer to get instant coaching from Nova.

Question 2Medium

Researchers surveyed a random sample of students at Jefferson High School about a proposal to start the school day one hour later. In the sample, 65% of students favored the proposal, with an associated margin of error of 3%.

Which of the following conclusions is best supported by the survey results?

Pick an answer to get instant coaching from Nova.

Question 3Hard

Researchers randomly selected 400 adults living in a city and recorded whether each adult meditated regularly, along with each adult's blood pressure. The adults who meditated regularly had a lower mean blood pressure than the adults who did not.

Which of the following conclusions is best supported by the study?

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The rest of Problem-Solving and Data Analysis

Evaluating Statistical Claims is one of 7 skills in Problem-Solving and Data Analysis. The ideas build on each other, so it pays to learn them as a set rather than in isolation. See how Problem-Solving and Data Analysis fits together.

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