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 sample mean $\bar{X}$ is equal to the population mean $\mu$ for all populations, regardless of the population distribution, sample size, or whether the population is finite or infinite. This is a property of the sample mean as an unbiased estimator of the population mean.

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

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