Question

A population consist of the number 2,3,4

a. Enumerate all possible sample size of 2.

b. Compute for the mean of each sample.

c. Find tye mean of the mean.

d. Find the standard deviation of the sample means.

e. Find the population mean.

f. Find standard deviation.

g. Find the standard error of the mean

Answer 1

$a:\left( 2,2 \right) ,\left( 2,3 \right) ,\left( 2,4 \right) ,\left( 3,2 \right) ,\left( 3,3 \right) ,\left( 3,4 \right) ,\left( 4,2 \right) ,\left( 4,3 \right) ,\left( 4,4 \right) \\b: \\\left( 2,2 \right) ,\bar{x}=2\\\left( 2,3 \right) ,\bar{x}=2.5\\\left( 2,4 \right) ,\bar{x}=3\\\left( 3,2 \right) ,\bar{x}=2.5\\\left( 3,3 \right) ,\bar{x}=3\\\left( 3,4 \right) ,\bar{x}=3.5\\\left( 4,2 \right) ,\bar{x}=3\\\left( 4,3 \right) ,\bar{x}=3.5\\\left( 4,4 \right) ,\bar{x}=4\\c:\\\mu _{\bar{x}}=\frac{2+2\cdot 2.5+3\cdot 3+2\cdot 3.5+4}{9}=3\\d:\\s=\sqrt{\frac{\left( 2-3 \right) ^2+2\cdot \left( 2.5-3 \right) ^2+3\cdot \left( 3-3 \right) ^2+2\cdot \left( 3.5-3 \right) ^2+\left( 4-3 \right) ^2}{9}}=0.57735\\e:\\\mu =\frac{2+3+4}{3}=3\\f:\\\sigma =\sqrt{\frac{\left( 2-3 \right) ^2+\left( 3-3 \right) ^2+\left( 4-3 \right) ^2}{3}}=0.816497\\g:\\s=\frac{\sigma}{\sqrt{2}}=0.57735\\\\$