Answer to Question #314706 in Statistics and Probability for Laiza

Question

a population consisits of four numbers (3,8,10,15) consider all the possible sample of size 2 that can be drawn without replacement from the population find the following

a.find the population mean

b. find the population varince

c.find the population standard deviation

d.find the possible sample of size 2 which can be drawn without replacement from this population

e.find the mean of the sampling distribution of means

f.find the varience of the sampling distribution of means

g.find the standard deviation of the sampling distribution of means .

Answer 1

$a:\\EX=\frac{3+8+10+15}{4}=9\\b:\\EX^2=\frac{3^2+8^2+10^2+15^2}{4}=99.5\\DX=EX^2-\left( EX \right) ^2=99.5-9^2=18.5\\c:\\\sigma X=\sqrt{DX}=\sqrt{18.5}=4.30116\\d:\\\left( 3,8 \right) ,\bar{x}=5.5\\\left( 3,10 \right) ,\bar{x}=6.5\\\left( 3,15 \right) ,\bar{x}=9\\\left( 8,10 \right) ,\bar{x}=9\\\left( 8,15 \right) ,\bar{x}=11.5\\\left( 10,15 \right) ,\bar{x}=12.5\\e:\\E\bar{x}=EX=9\\f:\\D\bar{x}=\frac{DX}{2}=\frac{18.5}{2}=9.25\\g:\\\sigma \bar{x}=\sqrt{D\bar{x}}=\sqrt{9.25}=3.04138\\$