Question

Find all the possible samples of size 2 which can be drawn with replacement from this population

A. Find the mean of the sampling distribution of means

B. Find the variance of the sampling distribution of means

C. Find the standard deviation of the sampling distribution of means

Answer 1

Given, Population is $2,3,6,7,9$

Sample size, $n=2$

The sampling distribution are as follows:-

(A). Mean of sampling distribution of means

=$\dfrac{2.5+4+4.5+5.5+4.5+5+6+6.5+7.5+8+2+3+6+7+9}{15}=\dfrac{81}{10}=8.1$

(B) Variance of sampling distribution of means

$=\sum\dfrac{(\bar{X}-X_i)^2}{10}$

$=\dfrac{(6.2)^2+(4.1)^2+(3.6)^2+(2.6)^2+(3.6)^2+(2.1)^2}{15}\\+\dfrac{(1.6)^2+(2.1)^2+(1.1)^2+(0.1)^2+(6.1)^2+(5.1)^2+(2.1)^2+(1.1)^2+(0.9)^2}{15}$

$=\dfrac{170.18}{15}=11.34$

(C) Standard deviation of sampling distribution of means is given by

=$\sqrt{\text{variance}}=\sqrt{11.34}=3.368$