### Aviation Applications Problem Set III MAT 211

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AVIATION APPLICATIONS PROBLEM SET III

This is the third of three aviation applications problem sets that you will complete for Math 211. It is worth 100 points or 10% of your course grade.

To complete the assignment, first save this Word document on your computer or memory device. Then complete each of the problems or questions by answering the problem or question in the Word document you saved.

Where appropriate, you must show your work and you must clearly indicate your answer. In some cases, showing your work can be done by pasting appropriate Excel or PHStat output into the Word file. Dont just paste the Excel or PHStat output into the documentalso clearly indicate your answer.

When you complete the assignment, save it, and then turn it in using the Blackboard Assignment Tool. If you have questions, please ask your instructor.

You will need the Excel data files below to complete this problem set.

ATL Taxi Times

Airline Prices

Air Fares

Wait Times PSIII

According to an article in News Daily (http://www.newsdaily.com/stories/n22504510-news-airlines-delays/), more than a quarter of U.S. Airlines flights were delayed in 2007. A flight departure is considered late if it departs 15 minutes or more beyond its scheduled departure time.

In a random sample of 500 Southwest Airlines flights departing Phoenix Sky Harbor Airport in January 2008, 141 departed 15 minutes or more later than scheduled. At the .05 level of significance, is there evidence that that the proportion of delayed Southwest Airlines departures from Phoenix in January 2008 is greater than 25%?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

Explain the meaning of the p-value in this problem.

If you do the hypothesis test from problem 1 again using this sample, do you get the same results? Give the p-value for this test, the results in terms of the null hypothesis, and the results in terms of the problem.

The true population proportion of delayed flights is 0.2535 or 25.35% so the null hypothesis that the proportion of delays is 25% or less is false. The results of part a of this problem should be, Do not reject the null hypothesis. What type error was made in part a, Type I or Type II? Explain your answer.

Suppose that as a somewhat frustrated frequent flyer that often uses the Atlanta Hartsfield Airport, you feel that taxi times there are longer than at other comparable U.S. airports. According to the U.S. Bureau of Transportation Statistics, the average taxi out time at Large Hub Airports in the U.S. was 18.5 minutes in 2007. Data File ATL Taxi Times gives taxi out times for a random sample of 100 flights in July 2007 at the Atlanta Hartsfield Airport.

At the .05 level of significance, is there evidence that the mean taxi time at the Atlanta Airport in July 2007 was greater than 18.5 minutes?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

Suppose you used a .01 level of significance. Would that change your decision in terms of the problem in part a? Explain why or why not.

1. A banner on the U.S. Airways website recently proclaimed that the airline was again number one in on-time departures. An airline flight departure is considered on-time if it departs less than 15 minutes beyond its scheduled departure time. Southwest Airlines is one of U.S. Airways chief competitors in Phoenix.

In a random sample of 500 U.S. Airways flights departing Phoenix Sky Harbor Airport in January 2008, 401 departed on-time. A similar sample of Southwest Airlines flights showed 359 departing on-time. At the .01 level of significance, is there evidence that the proportion of U.S. Airways flights departing on-time is significantly greater than the proportion of Southwest Airlines flights departing on-time?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

Are Southwest Airlines ticket prices cheaper? Data File Airline Prices gives the round-trip fare for 15 randomly selected Southwest Airlines city-pairs from www.southwest.com and from www.orbitz.com. The fares shown are the lowest round trip airfare available on June 26, 2008 for one adult round-trip departing on July 22, 2008 and returning on July 29, 2008.

At the .05 level of significance, is there evidence of a difference between Southwest air fares and airfares for the same city-pairs on Orbitz?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

Construct a 95% confidence interval estimate of the mean difference between Southwest fares and the fares shown on Orbitz.

Do the results of parts a and b agree? Explain your answer.

1. Suppose we want to conduct a hypothesis test to determine if there was a significant difference in U.S. air fares between the fourth quarter of 2006 and the fourth quarter of 2007. Data File Air Fares gives the average air fares at the 100 largest U.S. markets in the fourth quarter of 2007 and in the fourth quarter of 2006.

Would it be appropriate to use this data for the hypothesis test mentioned? Explain why or why not.

What would be a better data collection method for the hypothesis test in part a.

1. A number of airlines now charge a fee for booking a ticket directly with the airline either in person or by telephone. No fee is charged persons who book travel online. A survey conducted by SITA showed that in 2006, 47% of passengers booked their airline tickets online. In the 2007 this had increased to 49% and in 2008 to 57.6%.

Suppose the results are based on surveys of 2500 randomly selected passengers each year. At the .01 level of significance, is there evidence of a difference in the proportion of passengers who book tickets online among the three year groups?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

If appropriate, use the Marascuilo procedure and ? = .01 to determine which, if any, year groups are significantly different in the proportion of passengers who book tickets online.

Would the results change if samples of size 300 were used? Support your answer with appropriate calculations.

1. An airport with five security check points wants to compare the mean times that passengers have to wait to get through airport security between 8AM and 9AM on Monday morning among the five check points. Data File Wait Times PSIII gives the wait times for six randomly selected passengers arriving between 8 and 9 AM on a Monday morning at each of the check points.

Assuming the requirements of ANOVA are satisfied, at the .05 level of significance, is there evidence of a significant difference among the mean wait times at the five checkpoints?

Complete the following:

1. State H0.

2. State H1.

3. State the value of ?.

4. State the value of the test statistic.

5. State the p-value.

6. State the decision in terms of H0 and why.

7. State the decision in terms of the problem.

If appropriate, state which of the check points are significantly different in terms of mean wait times.

Based on the results of part a, if a passenger has a choice and wants to minimize wait time, which check point or check points should he or she choose?

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