Question

Delta Airlines is trying to determine if pilots are deliberately slowing down during a labor dispute. They know that their all their flights have a mean late time of 12.8 minutes with a standard deviation of 5.8 minutes. They took a random sample of 36 flights during the dispute and found they were 15.1 minutes late on average. Using a significance level of 0.05, is there any evidence to back their claim that the pilots are slowing down?

Answer 1

Given that all the Delta flights have a mean late time of =12.8 minutes with a standard deviation of =5.8.

And a random sample of n = 36 flights were studied during the dispute and found they were = 15.1 minutes late on average.

Based on the claim of the Delta airlines the hypotheses are:

Based on the hypothesis it will be a right-tailed test since population standard deviation is known hence Z- distribution is applicable for hypothesis testing.

Rejection region:

Based on the significance level and type of test the critical value for the rejection region is computed using excel formula for normal distribution which is =NORM.S.INV(1-0.05), Thus the Zc computed as 1.645.

So, reject Ho if Z> Zc = 1.645

Test Statistic:

P-value:

The P-value is computed using excel formula for normal distribution which is =1-NORM.S.DIST(2.379, TRUE) thus P-value computed as P-value =0.0087

Conclusion:

Since P-value < 0.05 and Z > Zc hence we can reject the null hypothesis and conclude that there is enough evidence to support the claim that pilots of Delta airlines are deliberately slowing down during a labor dispute.