In the same study of water quality, (n=145) samples were taken from streams having a high environmental
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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 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
\[
H_{0}:=10 \quad \text { versus } \quad H_{1}:=10
\]
at the \(5 \%\) level of signi cance.
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Related Book For
Introduction To Bayesian Statistics
ISBN: 9781118091562
3rd Edition
Authors: William M. Bolstad, James M. Curran
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