A statistician buys a pack of 10 new golf balls, and drops each golf ball from a height of one meter, and measures the height in centimeters it returns on the first bounce. The ten values are:79.9 80.0  78.9 78.5  75.6 80.5  82.5 80.1  81.6 76.7 Assume y, the height (in cm) a golf ball bounces when dropped from a one meter height is normal (µ, σ2), where the standard deviation σ = 2.

(a) Assume a normal (75, 102) prior for µ. Find the posterior distribution of

µ.

(b) Calculate a 95% Bayesian credible interval for µ.

(c) Perform a Bayesian test of the hypothesis H0 : µ ≥ 80 versus H1 : µ < 80 at the 5% level of significance.