$21.$ Gravetter$/$Wallnau$/$Forzano$,$ Essentials $-$ Chapter $4-$ End$-$of$-$chapter question $21$

For the following population of scores: $1,4,7$

Calculate the population mean and population variance.

$\backslash$mu $=$

$\backslash$sigma $^2=$

Complete the following table that lists all possible samples of n $=2$ scores from the population. Use the first three rows $($Samples a$$c$)$ as examples.

Sample

Score $1$

Score $2$

M $=\backslash$Sigma Xn

SS

SSn $-1$

SSn

a $111\mathrm{.}000\mathrm{.}000\mathrm{.}000\mathrm{.}00$

b $142\mathrm{.}504\mathrm{.}504\mathrm{.}502\mathrm{.}25$

c $174\mathrm{.}0018\mathrm{.}0018\mathrm{.}009\mathrm{.}00$

d $412\mathrm{.}50$

e $444\mathrm{.}00$

f $475\mathrm{.}50$

g $714\mathrm{.}00$

h $745\mathrm{.}50$

i $777\mathrm{.}00$

Calculate the mean for all values in the M column, SSn $-1$

column and in SSn

column. Which values match the parameters of the population? Identify those statistics that were biased. Identify those statistics that were unbiased.

Mean of M column $=$

$.$ This the mean $\backslash$mu of the population. The sample mean is estimate of $\backslash$mu $.$

Mean of SSn $-1$

column $=$

$.$ This the variance $\backslash$sigma $^2$ of the population. SSn $-1$

is estimate of $\backslash$sigma $^2.$

Mean of SSn

column $=$

$.$ This the variance $\backslash$sigma $^2$ of the population. SSn $-1$

is estimate of $\backslash$sigma $^2.$