In the context of estimating population proportions, what does a higher sample size result in?

A higher sample size results in a smaller margin of error when estimating population proportions. This is because increasing the sample size generally leads to more accurate and reliable estimates of the population parameter.

The margin of error is a reflection of the uncertainty associated with the estimate; it decreases as the sample size increases due to the law of large numbers, which states that larger samples tend to produce more stable estimates. As sample size increases, the standard error of the proportion—calculated using the formula for standard deviation of the sampling distribution—decreases. Consequently, when you compute the confidence interval for the population proportion, a smaller standard error results in a narrower interval, which directly translates to a smaller margin of error.

Thus, the choice indicating a smaller margin of error is the correct response, as it aligns with the relationship between sample size and the accuracy of statistical estimates.