9.2 The standard method of screening for a disease fails to detect the presence of the disease in 15% of the patients who actually do have the disease. A new method of screening for the presence of the disease has been developed.

A random sample of n = 75 patients who are known to have the disease is screened using the new method. Let T be the probability the new screening method fails to detect the disease.

(a) What is the distribution of v, the number of times the new screening

(b) Of these n = 75 patients, the new method failed to detect the disease in

(c) Use a beta (1,6) prior for x. Find g(.rrly), the posterior distribution of T.

(d) Find the posterior mean and variance.

(e) If x 2 .15, then the new screening method is no better than the standard method fails to detect the disease?

y = 6 cases. What is the frequentist estimator of T?

method. Test Ho : x 2 .15 versus HI : x < .15 at the 5% level of significance in a Bayesian manner.