Question

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?

A. The margin of error is multiplied by √0.5.
B. The margin of error is multiplied by √2.
C. The margin of error is multiplied by 0.5.
D. The margin of error is multiplied by 2.

Answer 1

When you cut the sample size in half, the margin of error is multiplied by √2.

Step-by-step explanation:

When you cut the sample size in half, the margin of error is multiplied by √2.

The margin of error is calculated by taking the standard error of the mean and multiplying it with the critical value for a given confidence level. The formula for the margin of error is:

Margin of Error = Critical Value * Standard Error of the Mean

Since the standard error of the mean is divided by √n, when you cut the sample size in half, the denominator becomes √(n/2), which is equal to √2 times the original standard error. Therefore, the margin of error is multiplied by √2.