Answer to Question #318617 in Statistics and Probability for jay

Question

Consider the population consisting of values

3, 5, and 7.

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

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

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

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

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

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

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

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

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

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

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

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