a$.$ Use the one$-$mean t$-$interval procedure with the sample mean, sample size, sample standard deviation, and confidence level given below to find a confidence interval for the mean of the population from which the sample was drawn.

b$.$ Obtain the margin of error by taking half the length of the confidence interval.

c$.$ Obtain the margin of error by using the formula $t_{\frac{}{2}}*\frac{s}{\sqrt[\phantom{2}]{n}}.$

$\stackrel{}{x}=24$

$n=36$

$s=5$

confidence level $=99\%$

Click here to view Page $1$ of the table of t$-$values with area alpha to its right.

Click here to view Page $2$ of the table of $t-$values with area alpha to its right.

a$.$ The $99\%$ confidence interval about $$ is to $($Round to three decimal places as needed.$)$

b$.$ The margin of error found by taking half the length of the confidence interval is $($Round to three decimal places as needed.$)$

c$.$ The margin of error found by using the formula is $($Round to three decimal places as needed.$)$