Question

A certain population is composed of the numbers 4, 5, 6 and 7. What is the mean of the sampling distribution of the sample mean if each sample contains two elements?

Answer 1

The mean of the population

$\mu=\cfrac{4+5+6+7} {4} =5.5.$

The mean of the sampling distribution of the sample mean is equal to the mean of the population, so

$\mu_{\bar x} =\mu=5.5.$