A marketing analyst for an owner of several auto dealerships knows that the demand for hybrid vehicles tends to fluctuate from year to year. This spring, the analyst will select a random sample of consumers who are planning to buy a new car this year, and she will determine the sample proportion who plan on buying a hybrid vehicle. This result will be used to determine a confidence interval for the population proportion of consumers who are planning to buy a new car that is a hybrid.
(a) The owner of the dealerships would like a 95% confidence interval for the population proportion described above that has a margin of error of .03. A previous survey asking the same question resulted in a confidence interval for the population proportion given by [.15, .20]. If the analyst decides to use this information in setting up her survey, what sample size will she need to use in order to meet the conditions specified for her interval?
(b) Due to time constraints, the analyst uses a sample size of 625 consumers and finds the sample proportion who indicate that they will buy a hybrid is p= 0.20 . She provides the owner of the dealerships with a confidence interval that has a margin of error of .04 (question: given the result from part (a), are you surprised that the margin of error is greater than .03 as requested in part (a)? Why or why not?). What level of confidence did the analyst use to arrive at this margin of error?