$(30$ Points$)$ Vital capacity is a measure of the amount of air that someone can exhale after taking a deep breath, Data was collected on brass players and a control group. Assume the population distributions were normal.

Table $1$: Table for Question $2$

Brass Player: $4\mathrm{.}7,4\mathrm{.}6,4\mathrm{.}3,4\mathrm{.}5,5\mathrm{.}5,4\mathrm{.}9,5\mathrm{.}3$

Control Group: $4\mathrm{.}2,4\mathrm{.}7,5\mathrm{.}1,4\mathrm{.}7,5\mathrm{.}0,-,-$

$($a$)(10$ Points$)$ Conduct a t test to determine whether the population mean for brass is

larger than that for control.

$($b$)$ Provide the $95\%$ confidence interval for the difference in the two population means.

$($c$)$ A esearcher claims that in theory the "spread$/$variance$"$ in the two populations is the same. Repeat step $1($and $2)$ utilizing this assumption with th

$1.$ You will have to present the R codes you have used and the outputs you get.

$2.$ You can use R markdown to solve the project $($easiest if you know R markdown$).$ Otherwise, you can use LaTex or MS Word $($or any other typing software$)$ to finish the project. If you use LaTex or MS Word, please don't forget to include your code and output in your document.