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

The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. Therefore, as the sample size increases, the standard deviation of the sampling distribution decreases. This means that for all sample sizes greater than 1, the standard deviation of the sampling distribution of the sample mean will be less than the population standard deviation of 50.

If a Population Standard Deviation Is Equal to 50, Then