Begin with the distribution Beta(7,3).
a. What "postulated proportion" would be associated with that distribution?
b. Using beta distribution quantiles, construct a 95% confidence interval for the success proportion of that distribution.
c. Let's say that this is survival data, as we did in class. In a data set where n = 20, 15 patients survive the appropriate time interval. Add that to the original beta distribution. What is the new beta distribution?
d. What is the success proportion associated with that distribution?
e. Construct a 95% confidence interval for that success proportion.
f. As the study progresses, you find of 20 additional patients, 15 survive in this group just like the last group. Add that to the original beta distribution. What is the new beta distribution?
g. What is the success proportion associated with that distribution?
h. Construct a 95% confidence interval for that success proportion.
i. How does the success proportion and confidence interval change as you get more data?