An airline reports that its flights are on time with an average delay of 15 minu

Question

An airline reports that its flights are on time with an average delay of 15 minutes with a variance of 150 based upon a study of 25 recent flights. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights was 22 minutes with a variance of 225. Based upon tha data was the disgruntled traveler correct in believing the variance of the delayed flights was greater than the reported variance of 150. Evaluate the disgruntled traveler claim by performing a hypothesis test with a significant level of .05. Assume the data is normally distributed.

Explanation / Answer

Let

sigma1 = population standard deviation of the sample from the airline

sigma2 = population standard deviation of the sample from the traveller

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   >=   1  
Ha:    sigma1^2 / sigma2^2   <   1  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical F, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    24         
df2 = n2 - 1 =    24          
F (crit) =    0.504093347         
              
Getting the test statistic, as              
s1 =    12.24744871          
s2 =    15          
              
Thus, F = s1^2/s2^2 =    0.666666667          

As F > 0.504, then we fail to reject Ho.

Hence, there is no significant evidence that the variance of the delayed flights was greater than the reported variance of 150 at 0.05 level. [CONCLUSION]

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