Question

Consider the set of even single-digit number {0, 2, 4, 6, 8}.

·       Make a list of possible sample size of 2 that can be taken from this sets of numbers

·       Construct the sampling distribution of the sample means for the size of 3 and the standard error.

Answer 1

Possible samples of size 2.

(0,2), (0,4), (0,6), (0,8), (2,4), (2,6), (2,8), (4,6), (4,8), (6,8)

Sampling distribution

Possible samples of size 3,

(0,2,4), (0,2,6), (0,2,8), (0,4,6), (0,4,8), (0,6,8), (2,4,6), (2,4,8), (2,6,8), (4,6,8)

$P(X=2)=P(X=2.67)=P(X=5.33)=P(X=6)=0.1$

$P(X=3.33)=P(X=4)=P(X=4.67)=0.2$

Standard Error

$\mu=∑xf(x)=4$

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

$=\sigma^2=1.33$

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