Question: State the decision rule that would be used to test the following hypotheses. Evaluate appropriate test statistic and state your conclusion.

(a) Ho: \(\mu \) = 120 versus Ha: \(\mu \) < 120; \(\bar{Y}\) = 114.2, n = 25. \(\sigma \) = 18, \(\alpha \) = 0.08

(b) Ho: \(\mu \) = 42.9 versus Ha: \(\mu \) \(\ne \) 42.9; \(\bar{Y}\) = 45.1, n = 16, \(\sigma \) = 3.2, \(\alpha \) = 0.01

(c) Ho: \(\mu \) = 14.2 versus Ha: \(\mu \) > 14.2; \(\bar{Y}\) =15.8, n = 9, \(\sigma \) = 4.1, \(\alpha \) = 0.13