6. Suppose a consumer advocacy group would like to conduct a survey to find the proportion of consumers who bought the newest model of a particular vehicle who were happy with their purchase.

(4 marks)How large a sample should they take so that a 90% confidence interval for the population proportion has a margin of error of 0.02? Assume that a preliminary sample suggests that 85% of consumers are satisfied.

(4 marks)Assuming that the results of the preliminary sample are not available, what is the most conservative estimate of the sample size that would limit the margin of error to within 0.05 of the population proportion for a 98% confidence interval?