Let the following sample of $8$ observations be drawn from a normal population with unknown mean and standard deviation: $10,24,22,28,25,12,20,26.($You may find it useful to reference the $t$ table.$)$

a$.$ Calculate the sample mean and the sample standard deviation. $($Round sample mean and sample standard deviation to $2$ decimal places.$)$

$\backslash$table$[[,],[$Sample mean,$20\mathrm{.}88],[$Sample standard deviation,$6\mathrm{.}33]]$

b$.$ Construct the $95\%$ confidence interval for the population mean. $($Round final answer to $2$ decimal places.$)$

$\backslash$table$[[$Confidence interval,$15\mathrm{.}48,$to$]]$

c$.$ Construct the $99\%$ confidence interval for the population mean. $($Round final answer to $2$ decimal places.$)$

$\backslash$table$[[$Confidence interval,$\mathrm{.}13\mathrm{.}04,$to$,28\mathrm{.}72]]$