Question: Suppose that both random variables X and Y are normally distributed. State the decision rule that would be used to test the following hypotheses. Evaluate the appropriate test statistic and state your conclusion.

a. \[{{H}_{0}}:\mu =120\] versus \[{{H}_{1}}:\mu <120;\bar{y}=114.2,n=25,\sigma =18,\alpha =0.08\]

b. \[{{H}_{0}}:\mu =42.9\] versus \[{{H}_{1}}:\mu \ne 42.9;\bar{x}=45.1,n=16,\sigma =3.2,\alpha =0.01\]