Consider Example A of Section 11.3.1 using a Bayesian model. As in the example, use a no...

Consider Example A of Section 11.3.1 using a Bayesian model. As in the example, use a normal model for the differences and also use an improper prior for the expected difference and the precision (as in the case of unknown mean and variance in Section 8.6). Find the posterior probability that the expected difference is positive. Find a 90% posterior credibility interval for the expected difference.

Reference

To study the effect of cigarette smoking on platelet aggregation, Levine (1973) drew blood samples from 11 individuals before and after they smoked a cigarette and measured the extent to which the blood platelets aggregated. Platelets are involved in the formation of blood clots, and it is known that smokers suffer more often from disorders involving blood clots than do nonsmokers. The data are shown in the following table, which gives the maximum percentage of all the platelets that aggregated after being exposed to a stimulus.