Question: The U.S. Department of Transportation defines an airline flight as being on time if it lands less than 15 minutes after the scheduled time shown in the carriers computerized reservation system. Cancelled and diverted flights are counted as late. A study of the 10 largest U.S. domestic airlines found Southwest Airlines to have the lowest proportion of late arrivals, at 0.1577 (Extracted from N. Tsikriktsis and J. Heineke, The Impact of Process Variation on Customer Dissatisfaction: Evidence from the U.S. Domestic Airline Industry, Decision Sciences, Winter 2004, 35(1), pp. 129 142). Suppose you were asked to perform a follow-up study for Southwest Airlines in order to update the estimated proportion of late arrivals. What sample size would you use in order to estimate the population proportion to within an error of

a. ±0.06 with 95% confidence?

b. ±0.04 with 95% confidence?

c. ±0.02 with 95% confidence?