The expected value of the sampling distribution of the sample mean $\bar { X }$ equals the population mean $\mu$ :
A) only when the population is normally distributed.
B) only when the sample size is large.
C) only when the population is infinite.
D) for all populations.

Question

Quizplus · Accepted Answer

The expected value of the sampling distribution of the sample mean is always equal to the population mean for all populations, regardless of the population distribution or sample size. This is a fundamental property of sampling theory.

The Expected Value of the Sampling Distribution of the Sample Xˉ\bar { X }Xˉ

The Expected Value of the Sampling Distribution of the Sample $\bar { X }$