The statistician buys ten used balls that have been recovered from a water hazard. He drops each from a height of one meter and measures the height in centimeters it returns on the rst bounce. The values are:

Assume that \(y\), the height (in \(\mathrm{cm}\) ) a golf ball bounces when dropped from a one-meter height, is normal \(\left({ }^{2}\right.\) ), where the standard deviation \(=2\).
(a) Assume a emphnormal( \(\left.7510^{2}\right)\) prior for . Find the posterior distribution of .
(b) Calculate a \(95 \%\) Bayesian credible interval for .
(c) Perform a Bayesian test of the hypothesis
\[
H_{0}: \quad 80 \text { versus } H_{1}: \quad\]
at the \(5 \%\) level of significance.

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