If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is called the:
A) standard error of $\bar { X }$ .
B) expected value of $\bar { X }$ .
C) sampling distribution of $\bar { X }$ .
D) normal distribution.

Question

Quizplus · Accepted Answer

The probability distribution of the sample mean $\bar { X }$ is called the sampling distribution of $\bar { X }$, which is the distribution of all possible sample means of size n taken from the same population. It is important because it allows us to make statistical inferences about the population mean based on the sample mean. The standard error of $\bar { X }$ is the standard deviation of the sampling distribution of $\bar { X }$ and the expected value of $\bar { X }$ is equal to the population mean. The normal distribution is a specific type of distribution and not necessarily relevant to the sampling distribution of $\bar { X }$.

If All Possible Samples of Size N Are Drawn from a Population