9.3 In the study of water quality in New Zealand streams documented in McBride et al. (2002) a high level of Campylobacter was defined as a level greater than 100 per 100 ml of stream water. n = 116 samples were taken from streams having a high environmental impact from birds. Out of these, y = 11 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 forr. Calculate the posterior distribution g(7riy).

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

(d) Find a 95% credible interval for T.

(e) Test the hypothesis 7r?

Ho : T = .lo versus HI : T # .1O at the 5% level of significance.