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Evaluating statistical claims — SAT practice questions

Evaluating statistical claims on the SAT Math test asks students to judge whether a survey or sample can support a conclusion about a whole population. Students must recognize convenience sampling, such as asking people at a school entrance, a bus stop, or one website, and see that a reported margin of error does not fix a biased sample. Questions usually present a short study and ask which choice best describes a limitation or a problem with using the result. Answer choices mix sampling bias with other issues such as sample size, and a common trap is treating a convenience sample as if it were random.

  • Section: Math 44 questions on the paper
  • 21 practice questions in the app

Sample questions

Question 1

A city council wants to estimate the proportion of all city residents who favor extending public transit hours. A staff member surveys people waiting at a downtown bus stop one morning. Which of the following best explains a problem with using this survey to estimate the opinion of all city residents?

  1. AA survey must include every city resident to estimate the proportion who favor extending transit hours.
  2. BThe sample overrepresents people who already use public transit.
  3. CThe survey was conducted on only one morning, so a proportion cannot be estimated from the responses.
  4. DThe survey cannot be used to estimate a proportion because opinions are not numerical.
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Answer: B — The sample overrepresents people who already use public transit.

People waiting at a bus stop are more likely to already use public transit and may have different opinions than residents overall, so the sample is not representative of the full population. A survey need not include every resident to estimate a proportion; conducting the survey on only one morning does not prevent estimating a proportion from the responses; and a proportion can be estimated from categorical (yes/no) opinions.

Question 2

A survey of adults in a city reports a margin of error of 0.5 percentage point, but the sample was drawn only from people who visited one specific website. Which of the following best describes a limitation of this survey’s results?

  1. AThe reported margin of error is too large for the results to be useful.
  2. BThe sample may not represent the population the survey describes.
  3. CThe margin of error was reported in percentage points rather than as a proportion.
  4. DThe margin of error should have been calculated using the number of adults in the city rather than the number of adults in the sample.
Show answer

Answer: B — The sample may not represent the population the survey describes.

The sample includes only visitors to one website, so it may not represent the adults in the city that the survey describes. A reported margin of error of 0.5 percentage point does not by itself make the results too imprecise to be useful. Reporting the margin of error in percentage points rather than as a proportion is not a limitation. The margin of error is calculated from the sample size rather than from the number of adults in the city.

Question 3

A student wants to estimate the percent of all students at a large high school who walk to school. She stands at the main entrance and asks the first 60 students she sees whether they walked. Of those 60, 9 say yes. Which of the following best describes a limitation of using her result to estimate the school-wide percent?

  1. AThe sample size of 60 is automatically too small for any useful estimate.
  2. BThe sample was not randomly selected, so it may not represent all students.
  3. CThe students were asked whether they walked rather than how far they live from the school.
  4. DThe result of 15%15\% was based on 60 responses rather than on the whole school.
Show answer

Answer: B — The sample was not randomly selected, so it may not represent all students.

Convenience sampling at one entrance is not a random sample of all students, so generalizing the 9/60=15%9/60 = 15\% result to the entire school is unreliable.

Practice 21 Evaluating statistical claims questions in the app

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