Using the central limit theorem for a Normally distributed variable, how would the standard deviation of the sample means for samples of size 200 be related to that of samples of size 3200?
A) It would be 1/16 as large.
B) It would be 1/4 as large.
C) It would be 4 times as large.
D) It would be 16 times as large.

Question

Quizplus · Accepted Answer

The standard deviation of the sample means (standard error) is inversely proportional to the square root of the sample size. Thus, increasing the sample size from 200 to 3200 (a factor of 16) reduces the standard error by a factor of 4 (the square root of 16).

Using the Central Limit Theorem for a Normally Distributed Variable