Question

3) The FAA is interested in knowing if there is a difference in the average number of on-time arrivals among four of the major airlines. The FAA believes that the number of on-time arrivals varies by airport. To control for this variation, they randomly select 100 flights for each of the major airlines at each of four randomly selected airports and record the number of on-time flights. The results are as follows 122+216 Points) Airline D 81 82 82 83 Airline A Airline B 82 84 84 86 Airline C Airport A Airport B Airport C Airport D 87 79 81 89 83 90 85 To answer questions a), b), and c), use 1 % level of significance, show all four steps of testing hypotheses procedure, and show complete work. Also compute samples means and P- values. Assume there is NO interaction effect a) Can the FAA conclude that there is a significant difference in the average number on time arrivals among the four major arlines? b) Is it necessary to conduct post-hoc tests such as Bonferoni and Tukeỵ on the 6 pairs of mean number of on-time arrivals for the four airlines in this problem Why or why not? c) Can the FAA conclude that there is a significant difference in the average number of on time arrivals among the four major airports? d) Is it necessary to conduct post-hoc tests such as Bonferroni and Tukey. on the 6 pairs of mean number of on-time arrivals for the four airports in this problem? Why or why not?

Answer 1

Answer:

To test :

H₀ : Row means are all equal

vs.

H₁ : Atleast one mean is different .

Test statistic :

F=MSR 10 Fas MSE

We reject the null hypothesis or H₀ if the observed value of
FF39(a)
,
FF39(a)
where ,
a-0.05

The value of the test statistic :  
F3,5320

Critical value :  
F39(a) 3.863

Now ,

F-3.5320 < 3.363

Hence we accept the null hypothesis or H₀ .

Thus the row means are all equal . Thus the airlines doesnot have a significant effect on the on-time arrivals .

To test :

H₀ : Coloumn means are all equal

vs.

H₁ : Atleast one mean is different .

Test statistic :

MSC Ho MSE

We reject the null hypothesis or H₀ if the observed value of   
FF39(a)
where ,
a-0.05

The value of the test statistic :  
F-6.7044

Critical value :  
F39(a) 3.863

Now ,

F-6.7044 3.863

Hence we reject the null hypothesis or H₀ .

Thus the coloumn means are not all equal . Thus the airports does have a significant effect on the on-time arrivals .