Applet Exercise In Exercise 16.7, we reconsidered our introductory example where the

Chapter 16, Problem 16.15

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Applet Exercise In Exercise 16.7, we reconsidered our introductory example where the number of responders to a treatment for a virulent disease in a sample of size n had a binomial distribution with parameter p and used a beta prior for p with parameters = 1 and = 3. We subsequently found that, upon observing Y = y responders, the posterior density function for p | y is a beta density with parameters = y + = y + 1 and = n y + = n y + 3. If we obtained a sample of size n = 25 that contained 4 people who responded to the new treatment, find a 95% credible interval for p. [Use the applet Beta Probabilities and Quantiles at www.thomsonedu.com/statistics/wackerly. Alternatively, if W is a beta-distributed random variable with parameters and , the R (or S-Plus) command qbeta(p,,) gives the value w such that P(W w) = p.]