Airlines face the challenging task of keeping their planes on schedule. One key measure is the number of minutes a plane deviates from the targeted arrival time. Ideally, the measure for each arrival will be zero minutes, indicating that the plane arrived exactly on time. However, experience indicates that even under the best of circumstances there will be inherent variability. Suppose one major airline has set standards that require the planes to arrive, on average, on time, with a standard deviation not to exceed two minutes. To determine whether these standards are being met, each month the airline selects a random sample of 12 airplane arrivals and determines the number of minutes early or late the flight is. For last month, the times, rounded to the nearest minute, are
|
3
|
-7
|
4
|
2
|
-2
|
5
|
11
|
-3
|
4
|
6
|
-4
|
1
|
(a) State the appropriate null and alternative hypothesis for testing the standard regarding the mean value. Test the hypothesis using a significance level equal to 0.05. What assumption will be required?
(b) State the appropriate null and alternative hypotheses regarding the standard deviation. Use the sample data to conduct the hypothesis test with a = 0.05.
(c) Discuss the results of both tests. What should the airline conclude regarding its arrival standards? What factors could influence the arrival times of flights?