For each of the following, calculate the degrees of freedom ( \(d f\) ) and determine the critical values of \(t\) (assume \(\alpha=.05\) ).

a. \(N_{1}=21, N_{2}=21, \mathrm{H}_{1}: \mu_{1} eq \mu_{2}\)

b. \(N_{1}=14, N_{2}=14, \mathrm{H}_{1}: \mu_{1} eq \mu_{2}\)

c. \(N_{1}=4, N_{2}=4, \mathrm{H}_{1}: \mu_{1}>\mu_{2}\)

d. \(N_{1}=32, N_{2}=32, \mathrm{H}_{1}: \mu_{1}<\mu_{2}\)