16.2 We are going to observe the number of "successes" in n = 100 independent trials. We have prior experience and believe that a beta(6,14) summarizes our prior experience. However, we consider that our prior experience may have occurred under different conditions, so our prior may be bad. We decide to use a mixture prior where go(n-) is the beta(6,14) and gI(T) is the beta(1,l)

distribution, and the prior probability P(I = 0) = .95. Suppose we take a random sample of n = 100 and observe y = 36 successes.

(a) Use BinoMixpmac or the equivalent R function to find the posterior

(b) Find a 95% Bayesian credible interval for n-.

(c) Test the hypothesis HO : n- 5 .5 vs. HI : n- > .5 at the 5% level of distribution g(n-ly).

significance.