For each of the following situations, calculate the population standard error of the mean \(\sigma \mathrm{X}^{-}\)and the \(z\)-statistic \((z)\), make a decision about the null hypothesis, and indicate the level of significance.

a. \(\mathrm{X}^{-}=4.00 ; \mu=2 ; \sigma=6 ; N=36\)

b. \(\mathrm{X}^{-}=24.52 ; \mu=19.76 ; \sigma=10.93 ; N=23\)

c. \(\mathrm{X}^{-}=8.11 ; \mu=10.12 ; \sigma=3.28 ; N=19\)

d. \(\mathrm{X}^{-}=4.54 ; \mu=3.89 ; \sigma=2.32 ; N=33\)