All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?
A) The population mean.
B) It is larger than the population mean.
C) It is smaller than the population mean.
D) It cannot be estimated in advance.

Question

Quizplus · Accepted Answer

The mean of the sample means is equal to the population mean, as stated by the central limit theorem. This theorem states that as the sample size increases, the distribution of sample means becomes normal, centered around the population mean. Therefore, the mean of the sample means is the same as the population mean.

All Possible Samples of Size N Are Selected from a Population