Question

Consider the set of even single-digit number {0,2,4,6,8}. Construct the sampling distribution of the sample means for the size of 3 and the standard error.

Answer 1

Possible samples

Sampling distribution

$P(\mu_3=2.00)=P(\mu_3=2.67)=P(\mu_3=5.33)=P(\mu_3=6.00)=0.1$

$P(\mu_3=3.33)=P(\mu_3=4.00)=P(\mu_3=4.67)=0.2$

Standard Error

$\mu=∑xf(x)=4$

$\sigma=\sqrt{∑x^2f(x)-4^2}=\sqrt{17.33-4^2}$

$=\sigma^2=1.33$

$S.E=\frac{\sigma}{\sqrt{n}}=\frac{\sqrt{1.33}}{\sqrt{3}}=0.665$