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 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. \(\mathrm{X}^{-}=14.01 ; \mu=18.34 ; s=8.82 ; N=17\)

b. \(\mathrm{X}^{-}=6.41 ; \mu=5.72 ; s=1.21 ; N=15\)

c. \(\mathrm{X}^{-}=78.89 ; \mu=70 ; s=23.54 ; N=13\)

d. \(\mathrm{X}^{-}=471.76 ; \mu=500 ; s=48.51 ; N=25\)