Suppose you take a sample of size 4 from a population with a mean of 70 and a standard deviation of 10.Based on such a sample,what are the mean and standard deviation of the sampling distribution of $\bar { x }$
?
A) $\mu _ { \bar { x } }$ = 70, $\sigma _ { \bar { x } }$ = 5
B) $\mu _ { \bar { x } }$ = 70, $\mu _ { \bar { x } }$ = 2.5
C) $\mu _ { \bar { x } }$ = 17.5, $\mu _ { \bar { x } }$ = 5
D) $\mu _ { \bar { x } }$ = 17.5, $\mu _ { \bar { x } }$ = 10
E)Cannot be determined unless the sample size is at least 30.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of $\bar{x}$ is equal to the population mean ($\mu_{\bar{x}} = \mu = 70$), and the standard deviation of the sampling distribution of $\bar{x}$ ($\sigma_{\bar{x}}$) is equal to the population standard deviation ($\sigma$) divided by the square root of the sample size ($n$), which is $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{4}} = 5$.

Suppose You Take a Sample of Size 4 from a Population