Question sample
| Sample | Percent in favor | Margin of error |
| A | 52% | 4.2% |
| B | 48% | 1.6% |
The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?
Sample A had a smaller number of votes that could not be recorded.
Sample A had a higher percent of favorable responses.
Sample A had a larger sample size.
Sample A had a smaller sample size.
Sample Percent in favor Margin of error A 52% 4.2% B 48% 1.6% The results of
Hard-difficulty · SAT Math · Inference from Samples & Margin of Error — Sample size effects. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. Sample size is an appropriate reason for the margin of error to change. In general, a smaller sample size increases the margin of error because the sample may be less representative of the whole population.
Choice A is incorrect. The margin of error will depend on the size of the sample of recorded votes, not the number of votes that could not be recorded. In any case, the smaller number of votes that could not be recorded for sample A would tend to decrease, not increase, the comparative size of the margin of error. Choice B is incorrect. Since the percent in favor for sample A is the same distance from 50% as the percent in favor for sample B, the percent of favorable responses doesn’t affect the comparative size of the margin of error for the two samples. Choice C is incorrect. If sample A had a larger margin of error than sample B, then sample A would tend to be less representative of the population. Therefore, sample A is not likely to have a larger sample size.
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