The compiling time $($seconds$)$ for four different programs has been measured. The result

is:

Program $1$: $5\mathrm{.}7,6\mathrm{.}3,6\mathrm{.}1,6\mathrm{.}0,5\mathrm{.}8,6\mathrm{.}2$

Program $2$: $6\mathrm{.}2,5\mathrm{.}3,5\mathrm{.}7,6\mathrm{.}0,5\mathrm{.}2,5\mathrm{.}5$

Program $3$: $5\mathrm{.}4,5\mathrm{.}0,6\mathrm{.}0,5\mathrm{.}6,4\mathrm{.}9,5\mathrm{.}2$

Program $4$:$3\mathrm{.}7,3\mathrm{.}2,3\mathrm{.}9,4\mathrm{.}0,3\mathrm{.}5,3\mathrm{.}6$

a$)$ Calculate CM and Total SS$.$

b$)$ Calculate SST and Total MST$.$

c$)$ Calculate SSE and Total MSE.

d$)$ Construct ANOVA table for the data.

e$)$ State the null and alternative hypotheses for an analysis of variance of $F-$test.

f$)$ Use the $p-$value approach to determine whether there is a difference in the four

programs means.