A two-stage clinical trial is planned for for testing H0: p=0.10 versus Ha: p>0.10, where p is the proportion of responders among patients who were treated by the protocol treatment. At the first stage, 15 patients are accrued and treated. If 4 or more responders are observed among the(first) 15 patients, H0 is rejected, the study is terminated, and no more patientsare accrued. Otherwise, another 15 patients will be accrued and treated in the second stage. If a total of 6 or more responders are observed among the 30 patients accrued in the two stages (15 in the first stage and 15 more in the seoncd stage), then H0 is rejected. For example, if 5 responders are found among the first stage patients, 15 second stage patients are accrued, and an additional 4 or more responders ( for a total of 6 or more among the 30) are identified, H0 is rejected and the study is over.
a) Use the binomial table to find the numerical value of alpha for this testing procedure.
b) Use the binomial table to find the probability of rejecting the null hypothesis when using this rejection region if p=0.30
c) For the rejection region defined above, find beta if p=0.30