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Sample Statistics and Margin of Error

Interpret what a poll's margin of error actually tells you about sampling variability.

22 original sample statistics and margin of error questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.

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Sample question 1 · hard

A poll of 1000 randomly selected voters found that 38% support a proposed policy, with a reported margin of error of 3%. Which choice best interprets the margin of error?

✓ It reflects the expected variability between this sample's result and the true population value, due to random sampling.
It measures the share of the respondents who were contacted but declined to answer the survey at all.
It guarantees that support across the whole population is exactly the 38% that this sample reported, with no room for sampling variation.
It proves that the poll's methodology contained no errors of sampling, wording, or interviewer conduct.

A margin of error describes the expected range of variation between a sample statistic and the true population value due to random sampling, not a guarantee, a proof of methodology, or a nonresponse rate.

Sample question 2 · hard

A poll of 200 randomly selected voters found that 58% support a proposed policy, with a reported margin of error of 5%. Which choice best interprets the margin of error?

✓ It reflects the expected variability between this sample's result and the true population value, due to random sampling.
It measures the share of the respondents who were contacted but declined to answer the survey at all.
It proves that the poll's methodology contained no errors of sampling, wording, or interviewer conduct.
It guarantees that support across the whole population is exactly the 58% that this sample reported, with no room for sampling variation.

A margin of error describes the expected range of variation between a sample statistic and the true population value due to random sampling, not a guarantee, a proof of methodology, or a nonresponse rate.

Sample question 3 · hard

A poll of 800 randomly selected voters found that 48% support a proposed policy, with a reported margin of error of 5%. Which choice best interprets the margin of error?

It proves that the poll's methodology contained no errors of sampling, wording, or interviewer conduct.
It guarantees that support across the whole population is exactly the 48% that this sample reported, with no room for sampling variation.
✓ It reflects the expected variability between this sample's result and the true population value, due to random sampling.
It measures the share of the respondents who were contacted but declined to answer the survey at all.

A margin of error describes the expected range of variation between a sample statistic and the true population value due to random sampling, not a guarantee, a proof of methodology, or a nonresponse rate.

Sample question 4 · hard

A poll of 200 randomly selected voters found that 39% support a proposed policy, with a reported margin of error of 2%. Which choice best interprets the margin of error?

It guarantees that support across the whole population is exactly the 39% that this sample reported, with no room for sampling variation.
✓ It reflects the expected variability between this sample's result and the true population value, due to random sampling.
It proves that the poll's methodology contained no errors of sampling, wording, or interviewer conduct.
It measures the share of the respondents who were contacted but declined to answer the survey at all.

A margin of error describes the expected range of variation between a sample statistic and the true population value due to random sampling, not a guarantee, a proof of methodology, or a nonresponse rate.

Sample question 5 · medium

A poll of randomly selected voters estimates that 46% support a measure, with a margin of error of 3 percentage points at the 95% confidence level. Which statement is the best interpretation?

Exactly 46% of all voters support the measure.
✓ Plausible values for the true level of support run from 43% to 49%.
Between 43% and 49% of the people polled supported the measure.
The poll is wrong 3% of the time.

The margin of error gives an interval around the estimate, here 46% ± 3%, which runs from 43% to 49% and plausibly contains the true population value. The 46% is exactly what the sample reported, so the interval describes the population rather than the sample.

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