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

a. \(\mathrm{X}^{-}=12.00 ; \mu=13 ; \sigma=5 ; N=25\)

b. \(\mathrm{X}^{-}=1.82 ; \mu=1.53 ; \sigma=.67 ; N=40\)

c. \(\mathrm{X}^{-}=6.64 ; \mu=5.94 ; \sigma=1.72 ; N=34\)

d. \(\mathrm{X}^{-}=76.29 ; \mu=87.71 ; \sigma=30.76 ; N=26\)