The Professor's Response

I also had a question on section 7.6 number 62.

See the professor's answer below.

Hi Natalie,

In this problem, we need to use the margin of error formula for the confidence interval for proportion to find an equation for n. That part is straightforward. However, the second part is not so easy.

We need to find values for p-hat and q-hat that when multiplied produce a maximum. This might remind you of those word problems from Algebra that read, "Find two numbers that sum to 1 and have a product that is a maximum..." In the video below, I have walked you through how that is done, but it is not something I would ask you to do on an exam. For these proportion, sample-size problems, we assume p-hat and q-hat are both 0.5. The video just explains why that is the case.

Professor McGuckian