In Exercise 4.115, we compared the average difference between actual and scheduled arrival times for December flights on two major airlines: Delta and United. Suppose now that we are only interested in the proportion of flights arriving more than 30 minutes after the scheduled time. Of the 1,000 Delta flights, 67 arrived more than \(30 \mathrm{~min}-\) utes late, and of the 1,000 United flights, 160 arrived more than 30 minutes late. We are testing to see if this provides evidence to conclude that the proportion of flights that are over 30 minutes late is different between flying United or Delta.

(a) State the null and alternative hypothesis.

(b) What statistic will be recorded for each of the simulated samples to create the randomization distribution? What is the value of that statistic for the observed sample?

(c) Use StatKey or other technology to create a randomization distribution. Estimate the p-value for the observed statistic found in part (b).

(d) At a significance level of \(\alpha=0.01\), what is the conclusion of the test? Interpret in context.

(e) Now assume we had only collected samples of size 75 , but got essentially the same proportions (5/75 late flights for Delta and 12/75 late flights for United). Repeating steps (b) through (d) on these smaller samples, do you come to the same conclusion?

Data From Exercise 4.115:
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.