Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes the plane to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, the airline decided to collect some data. Specifically, a random sample of 500 passengers was selected. Researchers observed the passengers and noted the number of bags each person carried on the plane. Out of the 500 passengers, 170 had more than one bag.
a. Based on this sample, develop and interpret a 98% confidence interval estimate for the proportion of the traveling population that would have been impacted had the "one-bag" limit been in effect. Discuss your result.
b. The domestic version of Boeing's 757 has a capacity for 220 passengers. Determine an interval estimate of the number of passengers you would expect to board the plane with more than one carry-on. Assume the plane is at its passenger capacity.
c. The operations manager would like to limit any inconvenience experienced by the airline's passengers. To that end, she decided to implement the newly proposed policy only if less than 30% of the passengers have more than one carry-on bag. Based on the sample results obtained and using the p-value approach, should the operations manager implement the newly proposed policy?