Suppose that a random sample of size \(n\) is drawn from a normal population distribution for which \(\sigma^{2}\) is assumed to be known and equal to the given value \(\sigma_{*}^{2}\). Define UMPU level \(\alpha\) tests of the following null hypotheses:

(a) \(H_{0}: \mu \leq \mu_{0}\) versus \(H_{a}: \mu>\mu_{0}\)

(b) \(H_{0}: \mu \geq \mu_{0}\) versus \(H_{a}: \mu<\mu_{0}\)

(c) \(H_{0}: \mu=\mu_{0}\) versus \(H_{a}: \mu eq \mu_{0}\)