. Consider the following situation: you are conducting a new method to detect a rare disease in patients, but require a sample of blood in order to conduct the procedure. Your measurement displays the proportion of a certain type of cell that is typically present in small amounts in your blood, where a higher measurement indicates strong potential for the disease.

a. Suppose that you'd like to know how precise your measurement is within 2.5% with 99% confidence. What sample size, in mL of blood, would you need in order to achieve this margin of error?

b. Suppose new information arose from a trusted source that the proportion you expect is around p = .15. How would this change your previous answer? Would using additional information be preferable in this scenario? Explain in the context of the problem.