In the previous two problems we found the posterior distribution of the slope of y on x, the rate of weevil infestation for endophyte infected and noninfected ryegrass Let 1 be the slope for noninfected ryegrass, and let 2 be the slope for infected ryegrass (a) Find the posterior distribution of 1 2 (b) Calculate a 95 credible interval for 1 2 (c) Test the hypothesis H0 1 2 0 versus H1 1 2 0 at the 10 level of significance

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Question: In the previous two problems we found the posterior distribution of the slope of y on x, the rate of weevil infestation for endophyte infected

In the previous two problems we found the posterior distribution of the slope of y on x, the rate of weevil infestation for endophyte infected and noninfected ryegrass. Let β1 be the slope for noninfected ryegrass, and let β2 be the slope for infected ryegrass

(a) Find the posterior distribution of β1 − β2.

(b) Calculate a 95 % credible interval for β1 − β2.

(c) Test the hypothesis H0 : β1 − β2 ≤ 0 versus H1 : β1 − β2 > 0 at the 10 % level of significance.

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