For each of the following situations, calculate a \(95 \%\) confidence interval for the mean ( \(\sigma\) not known), beginning with the step, "Calculate the degrees of freedom ( \(d f\) ) and identify the critical value of \(t\). ."

a. \(N=15, \bar{X}=6.00, s_{\bar{X}}=1.50\)

b. \(\quad N=24, \bar{X}=23.40, s_{\bar{X}}=1.73\)

\(\begin{array}{ll}\text {

c. } & N=13, \bar{X}=8.50, s_{\bar{X}}=.73 \\ \text {

d. } & N=19, \bar{X}=3.37, s_{\bar{X}}=.11\end{array}\)