You are going to decide whether \(A\) : \(\Theta\theta_{0}\). The gain in utility of choosing \(A\) instead of \(B\) is

In the first three subproblems below, you are given \(\theta_{0}, w_{A}\), and \(w_{B}\). Formulate the decision problem as a hypothesis test by indicating significance level \(\alpha\) and stating the alternative hypothesis \(H_{1}\).

(a) \(\theta_{0}=7, w_{A}=9, w_{B}=1\);

(b) \(\theta_{0}=-3, w_{A}=25, w_{B}=175\);

(c) \(\theta_{0}=100, w_{A}=1, w_{B}=100\).

(d) A pharmaceutical company has developed a medicine that changes certain blood values. They have two choices: to produce, or not to produce. If the mean change in that blood value is more than 17 , they earn 1 unit more by producing than by not producing. If the change is below 17 , they save 19 units by not producing. Convert this into statements about \(A, B\), and \(\theta_{0}\), and proceed as in the other subproblems.

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