Question

In the numbers {1, 3, 5, 7, 9} construct the following:

• List of possible sample size of 3 that can be taken from this sets of numbers
•   Sampling distribution of the sample means for the size of 3 and the standard error.

Answer 1

Possible samples of size three

(1,3,5), (1,3,7), (1,3,9), (1,5,7), (1,5,9), (1,7,9), (3,5,9), (3,5,7), (3,7,9), (5,7,9)

Sampling distribution

$P(\mu_3=3.00)=P(\mu_3=3.67)=P(\mu_3=7.00)=0.1$

$P(\mu_3=4.33)=P(\mu_3=5.00)=P(\mu_3=5.67)=0.2$

sampling error

$\sigma=\sqrt{26.33^2-4.996^2}=25.855$

$S.E.=\frac{25.855}{\sqrt{3}}=14.9274$