Answer to Question #318618 in Statistics and Probability for jay

Question

Consider the population consisting of values

3, 5, and 7.

a. List all the possible samples of size 2 that can be drawn from the population with replacement in the table below.

b. Find the mean of the sampling distribution of means.

c. Find the variance of the sampling distribution of the means

d. Find the standard deviation of the means

Answer 1

$\mu(3,5)=(3+5)/2=4$

$\mu(3,7)=(3+7)/2=5$

$\mu(5,7)=(5+7)/2=6$

$\mu(3,3)=(3+3)/2=3$

$\mu(5,5)=(5+5)/2=5$

$\mu(7,7)=(7+7)/2=7$

f(4)=f(6)=f(3)=f(7)=1/6

f(5)=2/6=1/3

$E(x)=\sum f\mu=1/6(4+6+3+7)+2/6\times5=5$

$\sigma^2=\sum f\mu^2-(\sum f\mu)^2=1/6(16+36+9+49)+2/6\times25-25=1.67$

$\sigma=\sqrt{\sigma^2}=\sqrt{1.67}=1.29$