Question

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 19 pounds for the summer weights and 24 pounds for the winter weights.

(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.

(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.

Answer 1

for the mean summer 95% confidence interval weight C. J. = 7 Į t22n-1 s 183 ± 1.984 x 19 Voo 186.770) = (179. 230 , We are 95% confident that mean summer weight including carry on luggage is lies between

(179.230 , 186.770) pounds. b) 95% c.f. for mean winter weight c- z = X Į txia.no - 190 Į 1.984 x 24 noo (185. 238 ,194. 762) = We are 95% confident that mean winter weigh including carry on luggage of this airlines passengers will lies between 185.238 to 194.762 pounds.