Question

A new treatment for AIDS is to be tested in a small clinical trial on 15 patients.The proportion p^ who respond to the treatment will be used as an estimate of the proportion p of (potential)responders in the entire population of AIDS patients. If in fact p=.2 and if the patients can be regarded as a random sample from the population, find the probability that:
a)p^=.2
b)p^=0

Answer 1

Let's try the binomial probability function, which states:

P(x) = (nCx)(p^x)[q^(n-x)]

For a): n = 15; x = 15 * .2 = 3; p = .2; q = 1 - p = 1 - .2 = .8
Therefore: P(3) = (15C3)(.2^3)(.8^12) = ?

Can you take it from here to finish?

For b): n = 15; x = 0; p = .2; q = .8
Therefore: P(0) = (15C0)(.2^0)(.8^15) = ?

Can you take it from here to finish?

I hope this will help.