SAT Math: Sample Estimates and Margin of Error Practice Questions
Use random-sample proportions and means to estimate population values, and interpret the uncertainty reported with an estimate. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
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1. In a random sample of 320 town residents, 208 support a proposed library. Using this sample proportion, how many supporters are estimated among the town's 20,000 residents?
Explanation. The sample proportion is 208/320 = 0.65. Applying that estimate to 20,000 residents gives 0.65(20,000) = 13,000. This is an estimate, not a count of every resident.
2. A survey reports an estimated population proportion of 55% with a margin of error of 4 percentage points. What is the lower endpoint of the reported interval, as a percent?
Explanation. Subtract the margin of error from the estimate: 55% - 4 percentage points = 51%. Percentage points describe the difference between two percentages, so no multiplication by 0.04 is needed.
3. A random-sample estimate of a population mean is 18.5 minutes, with a margin of error of 1.2 minutes. What is the upper endpoint of the reported interval, in minutes?
Explanation. Add the margin of error to the estimate: 18.5 + 1.2 = 19.7 minutes. The corresponding lower endpoint would be 17.3 minutes.
4. Two random samples use the same survey method and confidence level in a large population. All else equal, which sample size generally gives the smallest margin of error?
Explanation. Larger random samples generally produce more precise estimates when other conditions are comparable. Of the listed sample sizes, 800 is largest and therefore generally gives the smallest margin of error.
5. A reported interval estimates that between 46% and 52% of a town's residents support a policy. Which statement describes the interval correctly?
Explanation. The interval describes uncertainty in an estimate of the population proportion. Individual residents do not have support percentages in this binary survey. Its midpoint is an estimate, not a guaranteed exact population value, and margin of error is not a data-entry error rate.
6. Survey A estimates support at 52% with a margin of error of 3 percentage points. Survey B estimates support at 47% with a margin of error of 4 percentage points. How many percentage points long is the overlap of the two reported intervals?
Explanation. Survey A reports 49% to 55%, and Survey B reports 43% to 51%. Their overlap is 49% to 51%, a length of 51 - 49 = 2 percentage points. Overlap by itself does not establish an exact difference between population proportions.
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FAQ
Is a sample estimate an exact population count?
No. A random sample provides an estimate and sampling uncertainty. The reported margin of error summarizes a range around that estimate under the survey's method.
Does a larger sample remove every source of error?
No. A larger random sample generally reduces sampling variability. It does not automatically correct biased selection, unclear questions, or inaccurate responses.