All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn?

Step-by-step explanation:

Given that all else being equal, if you cut the sample size in half, whether this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn

We know that for a sample std error is calculated as

Std dev/\sq rt n

where standard deviation is that of population if given, otherwise that of sample.

Thus when sample size is halved, we have std error as

std dev/sq rt (n/2)

i.e. std error is multiplied by sqrt 2.

This in turn makes margin of error also multiplied by sq rt 2.