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.
Explanation
Correct answer: D.
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.
Desmos solution:
Note: The regression line shows that margin of error decreases as sample size increases, so the sample with the larger margin of error (A) must have the smaller sample size.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
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
Choice B is incorrect. Since the percent in favor for sample A is the same distance from 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
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.