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Exercise 4. Suppose that X = (X1, · · · , Xn) is a random sample...

Exercise 4. Suppose that X = (X1, · · · , Xn) is a random sample from a normal distribution with unknown mean µ and known variance σ^2 . We wish to test the following hypotheses at the significance level α. Suppose the observed values are x1, · · · , xn. For each case, find the expression of the p-value, and state your decision rule based on the p-values

a. H0 : µ = µ0 vs. Ha : µ not equal µ0.

b. H0 : µ = µ0 vs. Ha : µ > µ0.

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