A consumer testing organization obtained samples of size 12 from two brands of emergency flares, and measured the burning times. They are:

(a) We will assume that the observations come from normal(µA, σ2) and normal(µB, σ2), where σ2 = 32. Use independent normal (m, s2) prior distributions for µA and µB, respectively, where m = 20 and s2 = 82.
Find the posterior distributions of µA and µB, respectively.

(b) Find the posterior distribution of µA − µB.

(c) Find a 95% Bayesian credible interval for µA − µB.

(d) Perform a Bayesian test of the hypothesis H0 : µA − µB = 0 versus H1 : µA − µB = 0 at the 5% level of significance. What conclusion can we draw?