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SAT Math

Sample Statistics and Margin of Error

Sample Statistics and Margin of Error is a skill in the Problem-Solving and Data Analysis domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

9 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

A researcher randomly sampled 300 residents of a county with 18,000 residents and found that 45 of them had visited the county's new park. Based on this sample, about how many of the county's residents would be expected to have visited the park?
  1. A. 450
  2. B. 45
  3. C. 270
  4. D. 2,700 ✓

Correct answer: D. The sample proportion is 45/300 = 0.15, and applying this proportion to the full population gives 0.15 × 18,000 = 2,700 residents.

A poll estimates that 62% of a state's voters support a proposed measure, with a margin of error of plus or minus 3.5 percentage points. Based on this poll, which of the following is most likely true about the actual percentage of the state's voters who support the measure?
  1. A. It is likely between 58.5% and 65.5%. ✓
  2. B. It is exactly 62%.
  3. C. It is likely between 55% and 69%.
  4. D. It is likely greater than 65.5%.

Correct answer: A. The margin of error defines a symmetric interval around the estimate, so the true percentage is likely within 62% − 3.5% = 58.5% and 62% + 3.5% = 65.5%.

A pollster wants to reduce the margin of error of a survey while keeping the same method of random sampling. Which of the following changes would most directly help achieve this?
  1. A. Decrease the number of people randomly sampled.
  2. B. Increase the number of people randomly sampled. ✓
  3. C. Ask each respondent more questions during the survey.
  4. D. Replace random sampling with a convenience sample of easy-to-reach respondents.

Correct answer: B. Increasing the sample size, while keeping random sampling, generally reduces the margin of error, since larger random samples tend to produce more precise estimates of the population.

A random sample of 400 voters in a city of 150,000 registered voters found that 220 supported a proposed ballot measure. Based on this sample, what is the best estimate for the total number of registered voters in the city who support the measure?
  1. A. 82,500 ✓
  2. B. 55,000
  3. C. 220,000
  4. D. 66,000

Correct answer: A. Correct — the sample proportion is 220/400 = 0.55; applying this proportion to the full population gives 0.55 times 150,000, or 82,500.

A survey estimates that 42% of a population supports a new policy, with a margin of error of plus or minus 3 percentage points. Based on this survey, which of the following is NOT a plausible value for the true population support?
  1. A. 39%
  2. B. 46% ✓
  3. C. 41%
  4. D. 44%

Correct answer: B. Correct — the margin of error establishes a plausible range from 42% minus 3% to 42% plus 3%, or 39% to 45%; 46% falls outside this interval, so it is not a plausible value based on the survey.