The ministry of transport and communication is responsible for the enforcement of airline safety regulations and has become concerned about an apparent increase in accidents and near mishaps involving commercial aircraft. One area of concern is overloading due to passenger luggage exceeding regulated limits. Each passenger on overseas flight is allowed to carry 30 kg of luggage on board. To check adherences to this regulation, ministry officials conducted a spot check on passengers boarding both South African airways and British airways flights from Kenneth Kaunda international airport. The weight of luggage for each was recorded with the following results;
SOUTH AFRICAN AIRWAYS
No of passengers 138
Mean weight in kg 28.48
Standard deviation 9.45
Variance 89.3025
BRITISH AIRWAYS
No of passengers 184
Mean weight in kg 31.65
Standard deviation 7.21
Variance 63.4709
(a) construct 99 percent confidence intervals for the true mean weight of passengers luggage for each airline
( b) is there any reason to believe that either airline is routinely violating luggage regulations?