You are given the posterior distribution \(\theta \sim f(x)\), the significance \(\alpha\), and alternative hypothesis \(H_{1}\). Test, and decide between the competing hypotheses.

(a) \(\theta \sim \phi_{(7,2)}, \alpha=0.05\), and \(H_{1}: \theta>3\).

(b) \(\theta \sim \phi_{(9,2)}, \alpha=0.05\), and \(H_{1}: \theta>7\).

(c) \(\theta \sim \phi_{(8,3)}, \alpha=0.006\), and \(H_{1}: \theta<16\).

(d) \(\theta \sim t_{(7,2,3)}, \alpha=0.05\), and \(H_{1}: \theta>3\).

(e) \(\theta \sim t_{(9,2,5)}, \alpha=0.05\), and \(H_{1}: \theta>4\).

(f) \(\theta \sim t_{(24,3,1)}, \alpha=0.075\), and \(H_{1}: \theta<16\).