Question

Consider all possible samples of size 2 that can be drawn with replacement

from the population consists of numbers 1,2, and 3

a. mean of the sampling distribution

b. variance of the sampling distribution

c. standard deviation of the sampling distribution

 

Answer 1

The sampling distribution is shown in the figure-

Total sample N=9

(a) Mean $\bar{x} = \dfrac{ \sum x}{N}=\dfrac{18}{9}=2$

(b) Variance $\sigma^2=\dfrac{\sum (x-\bar{x})^2}{N}=\dfrac{3}{9}=0.33$

(c) Standard deviation $=\sqrt{\sigma^2}=\sqrt{0.33}=0.5773$