Because of safety considerations, in May 2003, the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months. The Alaska Journal of Commerce (May 25, 2003) reported that Frontier Airlines conducted a study to estimate mean passenger plus carry-on weights. They found a sample mean summer weight of 183 pounds and a winter sample mean of 190 pounds. Suppose that these estimates were based on random samples of 100 passengers and that the sample standard deviations were 20 pounds for the summer weights and 24 pounds for the winter weights. Ia USE SALT (a) Construct a 95% confidence interval (in pounds) for the population mean summer weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal places.) ( 176.080 x , 183.920 x )Ibs Interpret the interval. 0 We are 95% confident that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. 0 There is a 95% chance that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. 0 There is a 95% chance that the summer weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval. 0 We are 95% confident that the true mean summer weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. 0 There is a 95% chance that the true mean summer weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval. (b) Construct a 95% confidence interval (in pounds) for the population mean winter weight (including carry-on luggage) of Frontier Airlines passengers. (Round your answers to three decimal places.) ( 180.296 x , 189.704 X )lbs Interpret the interval. 0 There is a 95% chance that the true mean winter weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval. 0 There is a 95% chance that the winter weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. 0 We are 95% confident that the winter weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. We are 95% confident that the true mean winter weight (including carry-on luggage) of Frontier Airlines passengers falls within this interval. 0 There is a 95% chance that the winter weight (including carry-on luggage) of Frontier Airlines passengers falls directly in the middle of this interval. J (c) The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the condence interval estimates from parts (a) and (b). Based on the winter confidence interval, it is likely that Frontier Airlines will v 4 meet the new FAA recommendations for winter as the FAA recommendations are higher than the upper endpoint v J of the confidence interval. Based on the summer condence interval, it is likely that Frontier Airlines will v J meet the new FAA recommendations for summer as the FAA recommendations are higher than the upper endpoint v 4 of the condence interval
