For each of the following situations, calculate the degrees of freedom \((d f)\), identify the critical values (assume \(\mathbf{a}=.05\) [two-tailed]), calculate the standard error of the mean \(s\) \(\mathrm{X}^{-}\), calculate the \(t\)-statistic \((t)\), make a decision about the null hypothesis (reject, do not reject), and indicate the level of significance ( \(p>.05, p<.05, p<.01)\).

a. \(\mathrm{X}^{-}=75.00 ; \mu=65 ; s=18.00 ; N=9\)

b. \(\mathrm{X}^{-}=64.00 ; \mu=69 ; s=6.00 ; N=16\)

c. \(\mathrm{X}^{-}=75 ; \mu=63 ; s=.23 ; N=29\)

d. \(\mathrm{X}^{-}=78.51 ; \mu=67.92 ; s=18.53 ; N=23\)