Five drivers were selected to test drive $2$ makes of automobiles. The following table shows the number of miles per gallon for each driver driving each car.

$$table$[[,$Drivers$],[$Automobile$,1,2,3,4,5],[$A$,30,31,30,27,32],[$B$,36,35,28,31,30]]$

Consider the makes of automobiles as treatments and the drivers as blocks, test to see if there is any difference in the miles$/$gallon of the two makes of automobiles. Let $=\mathrm{.}05.$

$($a$)$ State the null and the alternative hypotheses

$($b$)$ Compute the sum of squares due to treatment $($SSTR$)$

$($c$)$ Compute the sum of squares due to block $($SSBL$)$

$($d$)$ Compute the total sum of squares $($SST$)$

$($e$)$ Find the value of the test statistic using the ANOVA table

$($f$)$ Using the $p-$value approach, what is your conclusion? Let $=0\mathrm{.}05.$