Question

consider all samples with the size of 5 from population 2 5 7 9 10 11 12

A. computer population mean

B. compute the population variance

C. computer population standard deviation

D. compute the mean of sampling distribution of the sample means and compare it the mean of the population.

E.compute the variance of sampling distribution of the sample means

F.compute a standard deviation of the sampling distribution of the sample mean

Answer 1

$A:EX=\frac{2+5+7+9+10+11+12}{7}=8\\B: EX^2=\frac{2^2+5^2+7^2+9^2+10^2+11^2+12^2}{7}=74.8571\\DX=EX^2-\left( EX \right) ^2=74.8571-8^2=10.8571\\C: \sigma X=\sqrt{DX}=\sqrt{10.8571}=3.29501$

D:

$E:{\sigma ^2}_{\bar{x}}=\frac{\sum{\left( \bar{x}_i-8 \right) ^2}}{21}=0.72381\\F:\sigma _{\bar{x}}=\sqrt{{\sigma ^2}_{\bar{x}}}=\sqrt{0.72381}=0.85077$