15.3 The moisture level of a dairy product is normally distributed with mean 15%

and unknown variance 02. A random sample of size 10 is taken and the moisture level measured. They are:

15.01 14.95 14.99 14.09 16.63 13.98 15.78 15.07 15.64 16.98

(a) What is the equation for the shape of the likelihood function of the variance u2 ?

(b) Use Jeffreys’ prior distribution for the variance 0’. Change the variable from the variance to the standard deviation to find the prior distribution for the standard deviation o.

(c) Find the posterior distribution of the variance u’.

(d) Change the variable from the variance to the standard deviation to find

(e) Find a 95% Bayesian credible interval for the standard deviation o.

(f) Test Ho : o 2 1.0 vs. HI : o > 1.0 at the 5% level of significance.

the posterior distribution of the standard deviation.