Question: Suppose you work for a survey research company. In a typical survey, you mail questionnaires to 150 companies. Of course, some of these companies might decide not to respond. Assume that the nonresponse rate is 45%; that is, each company's probability of not responding, independently of the others, is 0.45.
a. If your company requires at least 90 responses for a valid survey, find the probability that it will get this many. Use a data table to see how your answer varies as a function of the nonresponse rate (for a reasonable range of response rates surrounding 45%).
b. Suppose your company does this survey in two "waves." It mails the 150 questionnaires and waits a certain period for the responses. As before, assume that the nonresponse rate is 45%. However, after this initial period, your company follows up (by telephone, say) on the non respondents, asking them to please respond. Suppose that the nonresponse rate on this second wave is 70%; that is, each original non respondent now responds with probability 0.3, independently of the others. Your company now wants to find the probability of obtaining at least 110 responses total. It turns out that this is a difficult probability to calculate directly. So instead, approximate it with simulation.