Your are comparing two \(\gamma\) distributed variables \(\Theta \sim \gamma_{(k, l)}\) and \(\Psi \sim \gamma_{(m, n)}\) to decide between hypotheses \(H_{1}\) (as specified below) and \(H_{0}\), with significance \(\alpha\).

(a) \(\Theta \sim \gamma_{(7,70)}\), and \(\Psi \sim \gamma_{(4,80)}\). Significance \(\alpha=0.05\), and \(H_{1}: \Theta>\Psi\).

(b) \(\Theta \sim \gamma_{(9,20)}\), and \(\Psi \sim \gamma_{(11,20)}\). Significance \(\alpha=0.1\), and \(H_{1}: \Theta<\Psi\).

(c) Let the parameters in the Problem 14.b be 10 times as large. This corresponds to 10 times as many observations of each kind as in the previous problem. Do you think there should be a difference? Think about it for a while, and then calculate to see whether it matters or not!