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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.

AVIATION APPLICATIONS PROBLEM SET III

This is the third of three aviation applications problem sets that you will complete for MATH 211. To complete the assignment, save this Word document on your computer. Complete each of the problems. Fill in your answers on the Word document you saved. Where appropriate, show your work, and always indicate your answer clearly. In some cases, you will need to show your work. Do this by pasting appropriate Excel or PHStat data into the Word file, but be sure not just paste the Excel or PHStat data into the document. Remember if your answer is in the data example indicate it clearly. When you complete the assignment, save it to your computer or memory device, and then turn it in using the Blackboard Assignment Tool located in the appropriate module. If you have questions, please ask your instructor.

Use the zip file to download and save the Excel data files you will need to complete this assignment. The module section has the required zip file and download instructions.

1. One of the biggest issues facing e-retailers is the ability to reduce the proportion of customers who cancel their transactions after they have selected their products. It has been estimated that about 47% of airline customers cancel their purchases after they select their tickets. Suppose that an airline changed its web site so that customers could use a single-page checkout process rather than multiple pages. A sample of 500 customers who had selected their tickets was provided the new checkout system. Of these 500 customers, 210 cancelled their ticket purchases after selecting them.

a. At the .02 level of significance, is there evidence that the population proportion of customers who select their tickets and then cancel their transaction is less than 47%?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

b. Suppose that a sample of 100 customers (instead of 500 customers) were provided with the new checkout system and that 42 of those customers cancelled their transactions after selecting their tickets. At the .02 level of significance, is there evidence that the population proportion of customers who select tickets and then cancel their transactions is less than 47% with the new system?
Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

c. Compare the results of (a) and (b) and discuss the effect that sample size has on the outcome, and, in general, in hypothesis testing.

2. Excel file AptOntime gives the ontime flight departure percentages for 25 major U.S. airports for scheduled airlines for September 2009 and September 2010.

a. At the .05 level of significance, is there evidence of a difference in the mean ontime percentages for the 25 airports between September 2009 and September 2010?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

b. Construct a 95% confidence interval estimate of the difference in the mean ratings between September 2009 and September 2010.

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

3. Do Americans favor the use of full-body scanners at U.S. Airports? According to a poll conducted by CBS News in January 2010, 74% of Americans approved of the use of full-body scanners. In a later poll taken by CBS news in November 2010, 81% approved of the use of full-body scanners. The sample size for the January poll was 1216 and the sample size for the November poll was 1137. At the .05 level of significance is there evidence of a difference in the proportion of Americans favoring the use of full body scanners between January 2010 and November 2010?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

4. A CBS News survey conducted in November 2010 asked the question, “Do you think it would be justified for people of certain racial or ethnic groups to be subject to additional security checks at airport check points?” Respondents were categorized by political party and the table below shows the results.

Republican Democrat Independent Total
Justified 146 96 180 422
Not Justified 143 236 211 590
Depends 10 11 36 57
Don't Know 19 26 23 68
Total 318 369 450 1137

At the .01 level of significance, is there a relationship between political party affiliation and attitude toward people of certain racial or ethnic groups being subject to additional security checks at airport check points?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

5. Excel file Luggage gives the number of days it took to resolve a random sample of 50 complaints concerning airline baggage handling.

a. At the .05 level of significance, is there evidence that the mean time to resolve a complaint is greater than 30 days?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

b. What is the meaning of the p-value specifically in terms of this problem?

c. Without reworking the problem, would your conclusion change if a .01 level of significance was used? Explain your answer.

6. From each of four suppliers, a quality control technician collects a random sample of 10 rivets, then measures the number of pounds each will withstand before it fails. The data are shown in the table below.

Supplier A Supplier B Supplier C Supplier D
517 479 435 526
484 499 443 537
463 488 480 480
452 430 465 505
502 482 435 475
447 457 430 533
481 424 465 481
500 488 490 477
485 526 463 490
566 455 495 470

a. At the .05 level of significance, is there evidence of a difference in the mean breaking strengths of rivets from the four different suppliers?

Complete the following:
1. State H0.
2. State H1.
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 H0 and why.
7. State the decision in terms of the problem.

b. If appropriate, use the Tukey-Kramer procedure to determine which groups are significantly different.

c. If the strongest rivet is desired, which supplier should be used? Explain.
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