Question

- Statistics -

A report in USA Today claims that the average age of commercial jets in the US is 14 years. An executive of a large airline selects a sample of n=35 planes and finds that the average age of the planes is 18 years with a standard deviation of 2.7 years. Is there evidence to suggest that the average age of this airline’s planes is less than the national average? Conduct the test using a 5% level of significance. Make sure to include all of the steps of a hypothesis test.

Answer 1

H0: = 14

Ha: < 14

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 18 - 14 ) / ( 2.7 / √(35) )
t = 8.76

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 35-1) = 1.691 (From T table)
t > -t(α, n-1) = 8.76 > - 1.691

Result :- Fail to reject null hypothesis