##### (Answered)-8.2 Sensitivity analysis: In this exercise we will revisit the study from Exercise 5.2, in which 32.

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8.2 Sensitivity analysis: In this exercise we will revisit the study from Exercise 5.2, in which 32 students in a science classroom were randomly assigned to one of two study methods, A and B, with nA = nB = 16. After several weeks of study, students were examined on the course material, and the scores are summarized by {y¯A = 75.2, sA = 7.3}, {y¯B = 77.5, sb = 8.1}. We will estimate ?A = µ + d and ?B = µ - d using the two-sample model and prior distributions of Section 8.1. a) Let µ ~ normal(75, 100), 1/s2 ~ gamma(1, 100) and d ~ normal(d0, t 2 0 ). For each combination of d0 ? {-4, -2, 0, 2, 4} and t 2 0 ? {10, 50, 100, 500}, obtain the posterior distribution of µ, d and s 2 and compute i. Pr(d < 0|Y); ii. a 95% posterior confidence interval for d; iii. the prior and posterior correlation of ?A and ?B. b) Describe how you might use these results to convey evidence that ?A < ?B to people of a variety of prior opinions

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