For each of the following situations, calculate the degrees of freedom \((d f)\), identify the critical values (assume \(\mathrm{a}=.05\) [two-tailed]), calculate the \(t\)-statistic \((t)\), make a decision about the null hypothesis, and indicate the level of significance \((p>.05, p<\) \(.05, p<.01)\).

a. \(\mathrm{X}^{-}=12.71 ; \mu=16.49 ; s \mathrm{X}^{-}=1.91 ; N=9\)

b. \(\mathrm{X}^{-}=3.85 ; \mu=3 ; s \mathrm{X}^{-}=.42 ; N=16\)

c. \(\mathrm{X}^{-}=24.76 ; \mu=21.55 ; \mathrm{s} \mathrm{X}^{-}=1.27 ; N=12\)

d. \(\mathrm{X}^{-}=167.32 ; \mu=187.03 ; s \mathrm{X}^{-}=6.25 ; N=26\)