Suppose in a random sample of 20 items from a large population of 1000 items, 4 are found to be defective. Using a Standard Beta prior (see your Text p. 176) with parameters ? = 4 and ?=16, find a Bayesian credible region (an interval) for the unknown p which has posterior probability of 0.95 that p is in that interval. Pretty plz...... The work is required to use Excel. Solution As the prior has alpha =4 and beta = 16, as there are 4 defectives and 16 non- defectives, the posterior has alpha = 4+4=8 and beta = 16+16=32. Then, a credible Region with p=.95 has .025 in each tail. Then, the region is from betainv(.025,8,32) to betainv(.975,8,32) = (.092964,.33535).