The expected value of the sampling distribution of the sample mean $\bar { X }$ equals the population mean$\mu$:
A) when the population is normally distributed.
B) when the population is symmetric.
C) when the population size N 30.
D) for all populations.

Question

The expected value of the sampling distribution of the sample mean $\bar { X }$ equals the population mean$\mu$:
A) when the population is normally distributed.
B) when the population is symmetric.
C) when the population size N > 30.
D) for all populations.

Quizplus · Accepted Answer

The expected value of the sampling distribution of the sample mean equals the population mean for all populations, regardless of their distribution or size. This is a fundamental concept in statistics known as the law of large numbers.

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

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