For each of the following, calculate the degrees of freedom ( (d f) ) and determine the

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

a. \(N_{1}=5, N_{2}=5, \mathrm{H}_{1}: \mu_{1} eq \mu_{2}\)

b. \(N_{1}=12, N_{2}=12, \mathrm{H}_{1}: \mu_{1}<\mu_{2}\)

c. \(N_{1}=9, N_{2}=9, \mathrm{H}_{1}: \mu_{1} eq \mu_{2}\)

d. \(N_{1}=16, N_{2}=16, \mathrm{H}_{1}: \mu_{1}>\mu_{2}\)

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