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(A, 2) and normal(B, 2), where 2 32 Use independent normal (m, s2) prior distributions for A and B, respectively, where m 20 and s2 82 Find the posterior distributions of A and B, respectively (b) Find the posterior distribution of A B (c) Find a 95 Bayesian credible interval for A B (d) Perform a Bayesian test of the hypothesis H0 A B 0 versus H1 A B 0 at the 5 level of significance What conclusion can we draw

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Question: 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

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?

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