From data + prior to interval. Find \(I_{2 \alpha}^{\mu}\) and \(I_{2 \alpha}^{+}\). In addition, find \(I_{2 \alpha}^{\tau}\) and \(I_{2 \alpha}^{\sigma}\).

(a) Data: \(\{0.896,0.279,0.865,0.955,0.936,-0.046\}\); use a neutral prior. \(2 \alpha=0.05\).

(b) Prior: \(\kappa_{0}=6, m_{0}=150, v_{0}=5, s_{0}=10.2 \alpha=0.1\). Statistics: \(n=18\), \(\Sigma_{x}=2644.9, S S_{x}=3978.54\).

(c) Prior: \(\kappa_{0}=4, \Sigma_{0}=80, v_{0}=3, S S_{0}=27.2 \alpha=0.05\). You have 38 observations with average \(\bar{x}=19.8237\) and sample standard deviation \(s_{x}=\) 3.55143 .