SAT Math · Inference from sample statistics and margin of error · medium
A random sample of 400 voters found that 55% favor a candidate, with a reported margin of error of 3 percentage points. Which statement is…
A random sample of 400 voters found that 55% favor a candidate, with a reported margin of error of 3 percentage points. Which statement is most appropriately cautious given this information?
Answer and explanation
Answer: C: The true percentage of all voters favoring the candidate is plausibly between 52% and 58%.
The margin of error describes how far the true population percentage plausibly is from the sample estimate. With a sample percentage of 55% and a margin of error of 3 points, the plausible range is , or 52% to 58%, choice C. Choice A is too strong because a sample estimate is not exact. Choice B is false, since only 400 voters were surveyed, not the entire population. Choice D misreads the margin of error as a fixed bias; it is only a range of plausible sampling error, not a guarantee of a specific error. The wording "plausibly" matters.
More Inference from sample statistics and margin of error questions
- Question 51 · mediumSurvey A estimates that 52% of a population supports a proposal, with a margin of error of 4…
- Question 53 · hardA random sample of 1,000 adults found that 40% own a particular type of car, with a margin of…
- Question 326 · hardSurvey A samples 2,000 people and reports a margin of error of 2 percentage points. Survey B…
Learn the method behind questions like this one
The SAT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.