Sensitivity analysis: Thirty-two students in a science classroom were randomly assigned to one of two study methods, A and B, so that nA = nB = 16 students were assigned to each method. After several weeks of study, students were examined on the course material with an exam designed to give an average score of 75 with a standard deviation of 10. The scores for the two groups are summarized by {y¯A = 75.2, sA = 7.3} and {y¯B = 77.5, sb = 8.1}. Consider independent, conjugate normal prior distributions for each of θA and θB, with µ0 = 75 and σ 2 0 = 100 for both groups. For each (κ0, ν0) ∈ {(1,1),(2,2),(4,4),(8,8),(16,16),(3 2,32)} (or more values), obtain Pr(θA < θB|yA, yB) via Monte Carlo sampling. Plot this probability as a function of (κ0 = ν0). Describe how you might use this plot to convey the evidence that θA < θB to people of a variety of prior opinions.