Question

Given the population 5, 10, 15, 20, 25

a) How many samples of size 3, can be drawn with replacement from this population

b) Compute and tabulate the sampling distribution of the mean from samples of size 3.

c) Verify the results of the mean and variance of the sampling distribution of the mean. 

Answer 1

a) N=5

n=3

$Number = N^n = 5^3=125$

b)

The sampling distribution of the mean

c)

$Mean = \frac{5 \times 1 + 6.67 \times 3 +...+23.33 \times 3 + 25.0 \times 1}{125} = 15.0 \\ Variance = \frac{1}{125-1} ((5-15.0)^2+(6.67-15.0)^2+...+(23.33-15.0)^2+(25.0-15.0)^2) = 16.8$