The expected value of the sampling distribution of the sample mean equals the population mean μ :
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

The expected value of the sampling distribution of the sample mean  equals the population mean μ :
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.

Quizplus · Accepted Answer

The expected value of the sampling distribution of the sample mean equals the population mean μ for all populations, regardless of their distribution or size of the sample, according to the Central Limit Theorem. However, as the sample size increases, the sampling distribution becomes more normal, which leads to a more accurate estimation of the population mean.

The Expected Value of the Sampling Distribution of the Sample