If the sample size for a poll increases from 100 people to 400 people, the margin of error

Question

Quizplus · Accepted Answer

The margin of error in a poll is inversely proportional to the square root of the sample size. Therefore, when the sample size increases from 100 to 400 (which is a factor of 4), the margin of error decreases by a factor of 2 (the square root of 4), not by a factor of ½. My previous explanation contained an error in interpreting the relationship between sample size and margin of error. The correct relationship is that increasing the sample size decreases the margin of error, but the specific factor of decrease depends on the square root of the increase in sample size.

If the Sample Size for a Poll Increases from 100