Two school districts are used in a study to evaluate their performance at the high school level. Assume that the average scores on a national exam for a sample of public schools from each school district are given below. Dist. 1: sample size n1 = 8, sample mean 71 = 40 Dist. 2: sample size n2 = 24, sample mean yz = 26 Assume that yi ~ N(0;, o';), for i = 1,2 and o? = 14. In the following, if needed, you may assume a prior variance of 16. 1. Suppose that the two school districts are in two very different geographical regions and therefore have no similarity between them. Give a suitable prior of your choice for the parameters, and find the Bayesian estimate of 6 and 62, along with their standard deviations. 2 2. Suppose now that the two school districts are adjacent to each other, and that according to our knowl- edge, it is reasonable to assume they are similar. Give a suitable prior distribution for the parameters, and find the Bayesian estimate of 6 and #2, along with their standard deviations. 3. Comment on your answers in (i) and (ii), explaining the difference or similarity among them