Question

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

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 to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on 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, 321 had more than one bag. Complete parts a through d below.

b. A certain plane has a capacity for 447 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 the passenger was male or female. Out of the 1,000 passengers​ observed, 590 were male. Of this​ group,310 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.

d. Suppose the airline decides to conduct a survey of its customers to determine their opinion of the proposed​ one-bag limit. The plan calls for a random sample of customers on different flights to be given a short written survey to complete during the flight. One key question on the survey will​ be: "Do you approve of limiting the number of​ carry-on bags to a maximum of one​ bag?" Airline managers expect that only about 10​% will say​ "yes." 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 say​ "yes" with a margin of error ±0.09​?

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Answer 1

- Answer Given Let n be the no of passengers Nere Selected n = 1000 let X be the no. of passengers who camried more than one bag X 345 Let Þ be the proportion of the passengers who carried more than one bag þ. 3-45 95-. confidence interval for the no. of passengers who caried more than one bag ps [p-arhPuary (p-appr pt3 reg] (0-345-196 (1345(655, 0-34541.96 10:34.50te [0.345 -1.96 v0.295975 ,0-345 +1.96 10.995975 [0.345- 1.96 0.000225975 / 0.345+1.96V0-0008a5975 [0.345 -1.96(0.015032464 , 0-345+1-9660.015038464 [0.345 -0.029463631 ; 0.345+ 0.089463631] M. 374463631 100 1006 1000