$3.$ A tech company is comparing the processing speeds of two computer models. Ten computers were tested with Model $\backslash ($ A $\backslash ),$ and eight computers were tested with Model $\backslash ($ B $\backslash ).$ The processing speeds $($in gigahertz$)$ are recorded as follows:

i$.$ Does the computer model from Model $\backslash ($ A $\backslash )$ have better performance compared to the computer from Model $\backslash ($ B $\backslash )?$ Test at a significance level $\backslash (\backslash$alpha$=0\mathrm{.}05\backslash ).$

$(7$ marks$)$

ii$.$ Construct a $\backslash (95\backslash \%\backslash )$ confidence interval for the ratio of the variabilities of the processing speeds of two computer models.

$(5$ marks$)$

iii. What can you conclude about the results in part $($ii$)?$ Justify your answer. Hence, is the assumption you made in part $($i$)$ the best solution? Why?

iv$.$ Using the result in $($ii$)$ as an assumption, construct a $\backslash (98\backslash \%\backslash )$ confidence interval for the difference in means of the processing speeds of two computer models.