Hello,

I am very confused on how to solve the problem below. How do I find sample size n based off an 80% power? Also how do I find the standard deviation. Are these the right equations to use? and if so what is Z1-B , u1 and u2 equal to?

Consider a scenario where a drug company has 100 compounds for treating a type of cancer. Unbe-

knownst to the company, only 10 of the compounds are affective and the other 90 are of no value (i.e.

they do not work). For each compound, the company does an experiment and tests the affectiveness of

the compound using a hypothesis test with signicance level = 0:05. They choose a sample size for

each experiment so that the power of each test is 80% which is a standard value. What percentage of

the compounds found to be affective from the testing actually work? To answer this, do the following

parts:

a) For each test of a compound, state in words the null hypothesis for the statistical test.

b) How many of the affective compounds would you expect to be found to work? Why? (Round

your answer up to the nearest integer.)

c) How many of the non-affective compounds are expected to be found to work? Why?

d) From parts (b) and (c), what percent of compounds found to be affective actually work?

e) The term \false discovery rate" (FDR) is the proportion statistically significant results which are

actually false positives. What is the FDR in this example?

Thank you for your time,

Nivek