Hi everyone! I'm having some difficulty with this problem:
A pharmaceutical company has developed a new drug. Thirty monkey were given the drugs. Researchers intend to wait 6 weeks and then count the number of monkeys who have improved. Any inexpensive drug capable of being effective 60% of the time would be considered as a major breakthrough. Medications whose chances of success are < 50% are unlikely to have commercial potential.
The company hopes to avoid two errors: rejecting a drug that was actually marketable, and spending additional dollars on a drug that would in the end have chances < 50%. As a tentative decision rule, the project manager suggests that unless 16 or more monkey show improvement, research should be discontinued.
a) What are the chances that the rule will cause the company to reject the drug, even if the drug is 60% effective?
b) How often will the rule allow a 50% effective drug to be perceived as a major breakthrough.
I'm not sure where/how to start. I thought of finding the probability that 16 or more monkeys show improvement, but then i don't know how to incorporate the 60% effectiveness.
Any help is greatly appreciated. Thanks!