hypothesis tests

#1
im really bad with these kind of questions regarding null/alternative hypotheses and the probability of them being true/rejected

does any one have any suggesions on how i should approach these problems?

the current problem i am working on from my text states that:

Two medical researchers are independently studying the effectiveness of a new drug. Researcher A administers the drug to 12 patients and decides that she will reject the null hypothesis (that the drug has a 50/50 chance of being successful) only if all 12 are cured. Research B administers the drug to 20 patients and will reject the same null hypothesis if 15 or more are cured.

a) Assuming that Ho is true, what is the probability that both researchers will commit a type I error? [0.0000051]

b) a third researcher administers the drug to 25 patients and decided to form a decision rule such that alpha is less than or equal to 0.01. Assuming that the drug actually has an 80% probability of bring successful, what is the probability that the third researcher will nonetheless conclude that it is not effective? [0.220]
 

JohnM

TS Contributor
#2
a) = (.5)^12 * P(X >= 15)

P(X >= 15) is determined from the binomial distribution, with n=20 trials, p(success) = .5

b) if you have a binomial experiment with n=25 trials, and p(success)=0.5, p(fail)=0.5, at what number of successes, or higher, would you reject Ho at alpha=.01?

Now, with p(success)=0.8, what is the probability of getting the same number of successes or higher?