Answer:
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.
