Question

Does the airline you choose affect when you'll arrive at your destination? The dataset DecemberFlights contains the difference between actual and scheduled arrival time from 1000 randomly sampled December flights for two of the major North American airlines, Delta Air Lines and United Air Lines. A negative difference indicates a flight arrived early. We are interested in testing whether the average difference between actual and scheduled arrival time is different between the two airlines. (a) Define any relevant parameter(s) and state the null and alternative hypotheses. (b) Find the sample mean of each group, and calculate the difference in sample means. (c) Use StatKey or other technology to create a randomization distribution and find the p-value. (d) At a significance level of \(\alpha=0.01\), what is the conclusion of the test? Interpret the conclusion in context.

Short answer

Ultimately, you would need to calculate the p-value and compare it to the significance level (0.01) to determine the conclusion of your hypothesis test. Unfortunately, without the actual data this exercise cannot be completed in full. In general, if the p-value is less than 0.01, reject H_0: the average difference between actual and scheduled arrival time in United Air Lines is not significantly the same as Delta Air Lines. Otherwise, fail to reject H_0.

Step-by-step solution

Define Parameters and State Hypotheses

This study’s parameters would be the actual differences in arrival times for the two airlines, denoted as µ_1 for Delta Air Lines and µ_2 for United Air Lines. The null hypothesis (H_0) is that the difference in the average actual vs. scheduled arrival times (µ_1-µ_2) is the same for both airlines. People often state the null hypothesis as µ_1-µ_2 = 0 (which implies the same thing). The alternative hypothesis (H_a) is that µ_1-µ_2 ≠ 0 meaning there is a difference between the two airlines.

Find Sample Means and their Difference

Calculate the sample mean difference in arrival times for each airline. Then subtract the Delta Air Lines mean from the United Air Lines mean to get the observed difference in sample means, denoted as d_obs.

Carry Out a Permutation Test

Use statistical software to perform a permutation test and generate a randomization distribution. This will simulate the distribution under the null hypothesis and allows the calculation of the p-value.

Find the p-value

By comparing the observed mean difference (d_obs) to the randomization distribution, the p-value can be computed. The p-value shows the probability of getting a mean difference as extreme as d_obs or more under the null hypothesis

Interpret and Make Conclusion

At a significance level of \(\alpha=0.01\), if the p-value is less than \(\alpha\), reject the null hypothesis. This suggests that there is a significant difference in the flight arrival times between the two airlines. If the p-value is greater than \(\alpha\), fail to reject the null hypothesis, which would mean there is no significant difference between the flight arrival times of the two airlines.