AVIATION APPLICATIONS PROBLEM SET II I

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. Each problem is worth 10 points. To complete the assignment, first save this Word document on your computer. 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. Don’t just paste the Excel or PHStat output into the document—also 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 following Excel data files to complete Problem Set I. Depending on your configuration; you may need to log in to access the Content System files. The file downloaded from the Content System is a "Read Only" file. Save it to your computer or memory device in order to work with the file. (If you work in the "Read Only" file, you will loose all your work when you go to save the document.)

1. 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.
   1. 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:
      State H 0 .
      2. State H 1 .
      3. State the value of α.
      4. State the value of the test statistic.
      5. State the p-value.
      6. State the decision in terms of H 0 and why.
      7. State the decision in terms of the problem.

   2. Explain the meaning of the p-value in this problem.
2. I took another random sample of 500 Southwest Airlines departures from Phoenix in January 2008. In this sample, 126 of the 500 flights departed late.
   1. 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.
   2. 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.
3. 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 ( http://www.bts.gov/publications/bts_special_report/ 2008_008/html/table_04.html ). Data File ATL Taxi Times gives taxi out times for a random sample of 100 flights in July 2007 at the Atlanta Hartsfield Airport.
   1. 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:
      State H 0 .
      2. State H 1 .
      3. State the value of α.
      4. State the value of the test statistic.
      5. State the p-value.
      6. State the decision in terms of H 0 and why.
      7. State the decision in terms of the problem.

   2. 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.
4. 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.
   1. 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:
      State H 0 .
      2. State H 1 .
      3. State the value of α.
      4. State the value of the test statistic.
      5. State the p-value.
      6. State the decision in terms of H 0 and why.
      7. State the decision in terms of the problem.

5. 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 Orbitz: 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.
   1. 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:
      State H 0 .
      2. State H 1 .
      3. State the value of α.
      4. State the value of the test statistic.
      5. State the p-value.
      6. State the decision in terms of H 0 and why.
      7. State the decision in terms of the problem.

   2. For the test in part "a" to be valid, the pairs of values must have differences that are from a population that is approximately normal. Is this requirement satisfied? Support your answer with an appropriate display and explain your answer.
6. 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 Orbitz: 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.
   1. Construct a 95% confidence interval estimate of the mean difference between Southwest fares and the fares shown on Orbitz.
   2. Do the results of part a agree with the results of the hypothesis test you did in problem 5? Explain your answer.
7. Suppose we want to conduct a hypothesis test to determine if there was a significant difference in U.S. airfares between the fourth quarter of 2006 and the fourth quarter of 2007. Data File Air Fares gives the average airfares at the 100 largest U.S. markets in the fourth quarter of 2007 and in the fourth quarter of 2006.
   1. Would it be appropriate to use this data for the hypothesis test mentioned? Explain why or why not.
   2. What would be a better data collection method for the hypothesis test in part a.
8. With rising fuel costs, the amount of time it takes for an airliner to taxi from the departure gate to takeoff is a concern. Data File ATL Taxi Times gives taxi times for random samples of 100 flights in July 2000 and in July 2007 at the Atlanta Hartsfield Airport. At the .05 level of significance, is there evidence of a difference in the mean taxi times at the Atlanta Airport between July 2000 and July 2007?

   Complete the following:
   State H 0 .
   2. State H 1 .
   3. State the value of α.
   4. State the value of the test statistic.
   5. State the p-value.
   6. State the decision in terms of H 0 and why.
   7. State the decision in terms of the problem.

9. Data File US GA Accidents and Hours Flown contains data on the total General Aviation hours flown and the total number of accidents from 1977 through 2006. In problem set I, you constructed a scatter diagram with the number of hours flown on the horizontal axis and number of accidents on the vertical axis.
   1. Compute the coefficient of correlation between the number of hours flown and the number of accidents. Round your answer to three decimal places.
   2. Is the correlation between number of hours flown and number of accidents significant? Use a .05 level of significance.

      Complete the following:
      State H 0 .
      2. State H 1 .
      3. State the value of α.
      5. State the decision in terms of H 0 and why.
      6. State the decision in terms of the problem.

10. Data File US GA Accidents and Hours Flown contains data on the total General Aviation hours flown and the total number of accidents from 1977 through 2006. In problem 8, you computed the coefficient of correlation and conducted a test for significant correlation.
    1. Compute the least squares linear regression equation relating the number of hours flown to the number of accidents. Use three decimal places for both the slope and intercept.
    2. Estimate the number of general aviation accidents if 33,000,000 hours are flown. Round your answer to the nearest whole number.
    3. Would it be appropriate to use the regression equation you developed in part "a" to estimate the number of accidents if 50,000,000 hours are flown? Explain your answer.sssss

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