Most major airlines allow passengers to carry one luggage item (of a certain maximum size) and one personal item onto the plane. However, suppose the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on item per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had two carry-on items.

a. Based on this sample, develop and interpret a 95% confidence interval estimate for the proportion of the traveling population that would have been affected if the one-bag limit had been in effect. Discuss your result.

b. The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.

c. Suppose the airline also noted whether each passenger was male or female. Out of the 1,000 passengers observed, 690 were males. Of this group, 280 had more than one bag. Using these data, obtain and interpret a 95% confidence interval estimate for the proportion of male passengers in the population who would have been affected by the one-bag limit. Discuss.

d. Suppose the airline decides to conduct a survey of its customers to determine their opinion of the proposed one-bag limit. Airline managers expect that only about 15% will approve of the proposal. Based on this assumption, what size sample should the airline take if it wants to develop a 95% confidence interval estimate for the population proportion who will approve with a margin of error of $\pm$ 0.02?