9.4 In the same study of water quality, n = 145 samples were taken from streams having a high environmental impact from dairying. Out of these y = 9 had a high Campylobacter level. Let T be the true probability that a sample of water from this type of stream has a high Campylobacter level.

(a) Find the frequentist estimator for T.

(b) Use a beta (1,lO) prior for 7r. Calculate the posterior distribution g(7rly).

(c) Find the posterior mean and variance. What is the Bayesian estimator for

(d) Find a 95% credible interval for 7r.

(e) Test the hypothesis T?

Ho : T = .10 versus Hi : T # .10 at the 5% level of significance.