Two competing airlines, Alpha and Beta, fly a route between Des Moines, Iowa, and Wichita, Kansas. Each airline claims to have a lower percentage of flights that arrive late. Let p1 be the proportion of Alpha’s flights that arrive late and p2 the proportion of Beta’s flights that arrive late.
a. You are asked to observe a random sample of arrivals for each airline to estimate p1 – p2 with a 90% confidence level and a margin of error of estimate of .05. How many arrivals for each airline would you have to observe? (Assume that you will observe the same number of arrivals, n, for each airline. To be sure of taking a large enough sample, use p1 = p2 = .50 in your calculations for n.)
b. Suppose that p1 is actually .30 and p2 is actually .23. What is the probability that a sample of 100 flights for each airline (200 in all) would yield p̂1 > p̂2?