How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.

(MOE) the Margin of Error will decrease by the square root of 2

Step-by-step explanation:

The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400,  the Margin of Error will decrease by the square root of 2