The development of new drugs has to undergo stringent regulations resulting in long lead times and high research and development costs. Suppose that you are in charge of the federal agency that grants drug approvals and you wish to be convinced that a new drug is better than an existing one in terms of increasing the average life of patients.
(a) What are appropriate null and alternative hypotheses?
(b) Explain what type I and II errors are in this context and discuss their relative seriousness.
(c) How might you reduce the chances of these errors?
(d) What assumptions do you need to make to test the hypothesis in part (a)? How would you test the assumptions? Note that distributional assumptions will be tested.