$($a$)$ Compute four$-$week and five$-$week moving averages for the time series.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Week & Time Series Value & $\backslash$begin$\{$tabular$\}\{$l$\}$

$4-$Week $\backslash \backslash$

Moving $\backslash \backslash$

Average $\backslash \backslash$

Forecast

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

$5-$Week $\backslash \backslash$

Moving $\backslash \backslash$

Average $\backslash \backslash$

Forecast

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $18$ & & $\backslash \backslash$

$\backslash$hline $2$ & $22$ & & $\backslash \backslash$

$\backslash$hline $3$ & $19$ & & $\backslash \backslash$

$\backslash$hline $4$ & $24$ & & $\backslash \backslash$

$\backslash$hline $5$ & $18$ & $20\mathrm{.}75$ & $\backslash \backslash$

$\backslash$hline $6$ & $17$ & $20\mathrm{.}75$ & $20\mathrm{.}2\backslash \backslash$

$\backslash$hline $7$ & $20$ & $19\mathrm{.}5$ & $\backslash (\backslash$checkmark $\backslash )\backslash \backslash$

$\backslash$hline $8$ & $19$ & $\backslash ($ x $\backslash )$ & $\backslash (\backslash$checkmark $\backslash )\backslash \backslash$

$\backslash$hline $9$ & $22$ & $\backslash ($ x $\backslash )$ & $\backslash (\backslash$checkmark $\backslash )\backslash \backslash$

$\backslash$hline $10$ & $21$ & $\backslash ($ x $\backslash )$ & $\backslash ($ x $\backslash )\backslash \backslash$

$\backslash$hline $11$ & $16$ & $*$ & $*\backslash \backslash$

$\backslash$hline $12$ & $23$ & $\backslash (\backslash$checkmark $\backslash )$ & $\backslash ($ x $\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$($b$)$ Compute the MSE for the four$-$week moving average forecasts. $($Round your answer to two decimal places.$)$

Compute the MSE for the five$-$week moving average forecasts. $($Round your answer to two decimal places.$)$