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. A journal reported that an airline conducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of 183 pounds and a winter average of 190 pounds. Suppose that each of these estimates was based on a random sample of 100 passengers and that the sample standard deviations were 16 pounds for the summer weights and 21 pounds for the winter weights. LA USE SALT (a) Construct a 95% confidence interval for the mean summer weight (Including carry-on luggage) of this airline's passengers. (Use technology to calculate the critical value. Round your answers to three decimal places.) Interpret a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. O We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values. O We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. O There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is one of these two values. O There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values. O There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. (b) Construct a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers. (Use technology to calculate the critical value. Round your answers to three decimal places.) Interpret a 95% confidence Interval for the mean winter weight (including carry-on luggage) of this airline's passengers. O We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values. O There is a 95% chance that the true mean winter weight (Including carry-on luggage) of this airline's passengers is directly in the middle of these two values. O There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is one of these two values. O There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values. (c) The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from p
