Question

Take all possible samples of size 3 without replacement from population 0, 3, 6, 8, 9, 12, 15. Make a sampling distribution of Proportion odd numbers. Find its mean and Standard Deviation. Verify the properties.

Answer 1

N= 7

n=3

Number of samples $= \frac{N!}{n!(N-n)!}$

$= \frac{7!}{3!(7-3)!} = \frac{210}{6}=35$

The sampling distribution of Proportion odd numbers

Mean x $= \sum x \times P(x) = 0.428$

$SD = \sqrt{\sum (x^2 \times P(x) -(\sum x \times P(x))^2} \\ = \sqrt{0.238 -(0.428)^2} \\ = \sqrt{0.238-0.183} \\ = \sqrt{0.055} \\ =0.234$