Question

If the sample size is multiplied by 4, what happens to the standard deviation of the distribution of sample means?

Answer 1

Increasing the sample size by a factor of 4 or multiplying it by 4 is equal to increasing the standard error by 1/2.  Therefore, the interval will be half as varied.  This also works almost for population averages as lengthy as the multiplier from the t-curve doesn't modify much when increasing the sample size.