Question

A random sample of size 4 is taken with replacement from a population with population mean of 12 and population variance of 8. What is the variance of the sampling distribution.

Answer 1

Given, Population mean $\mu=12$ , population variance $\sigma^2=8$

sample size $n=4$

Sample standrad deviation $s= \sqrt{\sigma^2}\times \sqrt{n}=\sqrt{8}\times \sqrt{4}=\sqrt{32}$

Variance of sampling Distribution $s^2=(\sqrt{32})^2=32$