Suppose we use the entire sample of ten Poisson( ) observations as a single sample. We will start with the original prior from Computer Exercise 10.3 .

(a) Find the posterior given all ten observations using the Minitab macro PoisGamP or the R function poisgamp.

(b) What do you notice from Computer Exercises 10.3 10.5?

Data From Exercise 10.3

Suppose we start with a \(\operatorname{gamma}(62)\) prior for . Find the posterior distribution using the macro PoisGamP in Minitab or or the function poisgamp in \(\mathrm{R}\).
 
(c) Test the null hypothesis \(H_{0}: \quad 2\) vs \(H_{1}:>2\) at the \(5 \%\) level of signi cance.