22. Compute a 99% CI for m1  m2 using the data in Exercise 10.

Assume the same prior distribution used in Example 14.8, and assume that the data is a random sample from a normal distribution with mean m and s15.

a. Find the posterior distribution of m.

b. Find a 95% credibility interval for m.

c. Add four observations with average 110 to the data and nd a 95% con dence interval for m using the 19 observations. Compare with the result of (b).

d. Change the prior so the prior precision is very small but positive, and then recompute (a)
and (b).

e. Find a 95% con dence interval for m using the 15 observations and compare with the credibility interval of (d).