In the study of water quality in New Zealand streams, documented in McBride et al. (2002), a
Question:
In the study of water quality in New Zealand streams, documented in McBride et al. (2002), a high level of Campylobacter was de ned as a level greater than 100 per \(100 \mathrm{ml}\) 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 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
(b) Use a beta \((1\) 10) prior for . Calculate the posterior distribution \(g(y)\).
(c) Find the posterior mean and variance. What is the Bayesian estimator for ?
(d) Find a \(95 \%\) credible interval for .
(e) Test the hypothesis
\[
H_{0}:=10 \text { versus } H_{1}:=10
\]
at the \(5 \%\) level of signi cance.
Step by Step Answer:
Introduction To Bayesian Statistics
ISBN: 9781118091562
3rd Edition
Authors: William M. Bolstad, James M. Curran