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SAT Statistical Claims Practice

Use the study design to decide whether a result supports association, causation, or a claim about a larger population.

Practice statistical claims in Dolphin SATPractice questions
12-18 min practice time3 questions on pageProblem Solving and Data Analysis
Practice time12-18 min
Question bank3 questions
Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Hard
Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 30% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?
  1. The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.
  2. Those who responded to the poll were not a random sample of the population of the United States.
  3. There were not 50% “Yes” responses and 50% “No” responses.
  4. The show did not allow viewers enough time to respond to the poll.
Show answer and solution
Correct answerB. Those who responded to the poll were not a random sample of the population of the United States.

Solution walkthrough

  1. In order for the poll results from a sample of a population to represent the entire population, the sample must be representative of the population.
  2. A sample that is randomly selected from a population is more likely than a sample of the type described to represent the population.
  3. In this case, the people who responded were people with access to cable television and websites, which aren’t accessible to the entire population.
  4. Moreover, the people who responded also chose to watch the show and respond to the poll.
  5. The people who made these choices aren’t representative of the entire population of the United States because they were not a random sample of the population of the United States.
Why the other choices miss
Choices A, C, and D are incorrect because they present reasons unrelated to whether the sample is representative of the population of the United States.
Question 2 of 3Hard
A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students' accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?
  1. The 35 students in the sample
  2. All students at the school
  3. All middle school students in the city
  4. All students in the city
Show answer and solution
Correct answerB. All students at the school

Solution walkthrough

  1. The largest group to which the results of a study can be generalized is the population from which the random sample was chosen.
  2. In this case, the psychologist chose a random sample from all students at one particular middle school.
  3. Therefore, the largest group to which the results can be generalized is all the students at the school.
Why the other choices miss
Choice A is incorrect because this isn't the largest group the results can be generalized to. Choices C and D are incorrect because these groups are larger than the population from which the random sample was chosen. Therefore, the sample isn't representative of these groups.
Question 3 of 3Medium
A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts. What is the largest population to which the results of the survey can be generalized?
  1. All professors in the United States
  2. All history professors in the United States
  3. All history professors at all California State Universities
  4. All professors at all California State Universities
Show answer and solution
Correct answerC. All history professors at all California State Universities

Solution walkthrough

  1. Selecting a sample at random when conducting a survey allows the results to be generalized to the population from which the sample was selected, but not beyond this population.
  2. In this situation, the population that the sample was selected from is history professors from the California State Universities.
  3. Therefore, the largest population to which the results of the survey can be generalized is all history professors at all California State Universities.
Why the other choices miss
Choices A, B, and D are incorrect. Since the sample was selected at random from history professors from the California State Universities, the results of the survey can’t be generalized to all professors in the United States, all history professors in the United States, or all professors at all California State Universities. All three of these populations may use different texts and therefore may name different publishers.

Avoid these traps

Common mistakes on this skill

Turning association into causation

A relationship between two variables does not prove that changing one variable causes the other to change.

Confusing random selection and random assignment

Random selection supports generalization; random assignment supports causal comparisons between treatments.

Ignoring who was actually studied

A conclusion cannot automatically extend beyond the population represented by the sample.

Study plan

How to practice this skill in Dolphin

  1. Identify whether researchers only observed variables or assigned a treatment.
  2. Check whether participants were randomly selected from a population.
  3. Check whether participants were randomly assigned to groups.
  4. Match the strength of the conclusion to what the design can support.
Practice statistical claims in Dolphin SAT

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FAQ

Questions about SAT Statistical Claims Practice

What is the difference between association and causation?

Association means two variables move together. Causation means changing one variable directly produces a change in the other.

Why is random assignment important?

It helps make treatment groups comparable, reducing the effect of confounding variables and supporting causal conclusions.

Why is random selection important?

It helps a sample represent the larger population, making generalization more defensible.