A statistician buys a pack of 10 new golf balls, drops each golf ball from a height of one meter, and measures the height in centimeters it returns on the rst bounce. The ten 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 normal \(\left(7510^{2}\right)\) prior for . Find the posterior distribution of .
(b) Calculate a 95\% Bayesian credible interval for .

(c) Perform a Bayesian test of the hypothesis
\[
H_{0}: \quad 80 \text { versus } H_{1}:\]
at the \(5 \%\) level of signi cance.

Transcribed Image Text:

79.9 80.0 78.9 78.5 75.6 80.5 82.5 80.1 81.6 76.7