If a population standard deviation is equal to 50, then the sampling distribution of the sample mean, , will have a standard deviation that is less than 50 for all samples of size n 2.

Question

If a population standard deviation is equal to 50, then the sampling distribution of the sample mean,  , will have a standard deviation that is less than 50 for all samples of size n > 2.

Quizplus · Accepted Answer

This is true as per the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means becomes more normal and the standard deviation of the sampling distribution decreases. Therefore, for all sample sizes greater than 2, the standard deviation of the sample mean will be less than 50.

If a Population Standard Deviation Is Equal to 50, Then