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. \(\mathrm{X}^{-}=2.50 ; \mu=3.50 ; s \mathrm{X}^{-}=.67 ; N=9\)

b. \(\mathrm{X}^{-}=25.00 ; \mu=20 ; s \mathrm{X}^{-}=2.00 ; N=16\)

c. \(\mathrm{X}^{-}=.78 ; \mu=.59 ; \mathrm{X}^{-}=.09 ; N=14\)

d. \(\mathrm{X}^{-}=4.91 ; \mu=2.84 ; s \mathrm{X}^{-}=.60 ; N=21\)