The central limit theorem states that if the population is normally distributed, then the .
A) mean of the population can be calculated without using samples
B) standard error of the mean will not vary from the population mean
C) sampling distribution of the mean will vary from sample to sample
D) sampling distribution of the mean will also be normal for any sample size

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the mean will be normally distributed, regardless of the population distribution, as the sample size becomes large. However, it does not require the population to be normally distributed for this to hold true. The statement in D is a common misunderstanding; the correct interpretation is that if the population is normally distributed, then the sampling distribution of the mean will be normal for any sample size, not just large ones.

The Central Limit Theorem States That If the Population Is