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 2 8, sample mean 331 = 40 Dist. 2: sample size M = 24, sample mean 372 = 26 Assume that 371- ~ N (91, 02 z-), for 2' = 1, 2 and 02 = 14. In the following, if needed, you may assume a prior variance of 16. 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 nd the Bayesian estimate of 01 and 02, along with their standard deviations