Do this problem by hand$/$calculator$.$

$($It is okay to use to compute the sample mean and standard deviation$)$

Q$2\mathrm{.}1$ Two computers often ar

e compared by running a collection of various "benchmark" programs and recording the difference in CPU time required to complete the same program. Six benchmark programs, run on two computers, produced the following table of CPU times $($in minutes$).$

Benchmark Program

Computer $123456$

$11\mathrm{.}121\mathrm{.}731\mathrm{.}041\mathrm{.}861\mathrm{.}472\mathrm{.}10$

$21\mathrm{.}151\mathrm{.}721\mathrm{.}101\mathrm{.}871\mathrm{.}462\mathrm{.}15$

$($Assume CPU times form a normal distribution.$)$

$($a$)(7$pts$)$ Do the data provide sufficient evidence to indicate a difference in mean CPU times required for the two computers to complete a job? Test using

$$

$=$

$0\mathrm{.}05$

$\backslash$alpha $=0\mathrm{.}05.$

$($b$)(3$pts$)$ Find bounds for the associated p$-$value from the T$-$table.

$($c$)(3$pts$)$ Find a $95\%$ confidence interval for the difference in mean CPU time required for the two computers to complete a job.