Question $1\mathrm{.}1$

The length of the skulls of $12$ collected fossil skeletons of an extinct species of bird has sample mean $5\mathrm{.}68cm.$ The standard deviation of the sample is $0\mathrm{.}29cm.$ Assuming that

such measurements are normally distributed, find a $95\%$ confidence interval for the mean length of the skulls of this species of bird. Create $R$ vector $Cl$ of length two, so that the

first and the second entries are the lower and the upper end points of your confidence interval, respectively.

Do not round your answer.

Make sure R code passes ALL test provided by the following code:

## check whether $Cl$ is a numeric vector of length $2$

if $($test$\_$that$($desc$="",$ code$=\{$

expect$\_$equal$($ is$.$numeric$($CI$),$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$Sorry$,Cl$ is not a numeric vector."$)$

if $($test$\_$that$($desc$="",$ code

expect$\_$equal$($ length$($CI$)==2,$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$Sorry$,Cl$ is not of length $2.")$

And

## check whether whether $6$ th and $7$th dec. digits of $CI[1]$ and $CI[2]$ are $27$ and $72,$ respectively

if $($test$\_$that$($desc$="",$ code

expect$\_$equal$(($floor$($CI$[1]*10^7)\%100==27),$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$Sorry$,$ your $Cl$ is incorrect."$)$

if $($test$\_$that$($desc$="",$ code$=\{$

expect$\_$equal$(($floor$(\{$:$CI[2{]}^{**}{10}^{{?}^{{?}^{?}}}7)\%100==72),$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$Sorry$,$ your $Cl$ is incorrect."$)$