Question

Random samples of size 4 are drawn wigh replacement from a finite population 3,6,9. How many possible samples of size 4 are possible? Find the mean of the sample means.

Answer 1

$\begin{pmatrix} N \\ n \end{pmatrix}$ =$\begin{pmatrix} 3, 4 \end{pmatrix}$ =12 The possible sample size of 4 that can be drawn is 12

From this we can get the mean for each sample drawn

Since it's with replacement

3,6,9= (3+6+9)/4=18/4=4.5

3,6,9= (3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

3,6,9=(3+6+9)/4=18/4=4.5

The total of the mean becomes

4.5+4.5+4.5+4.5+4.5+4.5+4.5+4.5+4.5+4.5+4.5+4.5= 54

The mean of the sample means is equal to

54/12 =4.5