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Quantitative Methods – MJ8 – 03-30-21 – Sect1 Module 7
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Sheet4

Remember to submit your work following the file naming convention FirstInitial.LastName_M01.docx. For example, J.Smith_M01.docx. Remember that it is not necessary to manually type in the file extension; it will automatically append.

Start by reading and following these instructions:

1. Quickly skim the questions or assignment below and the assignment rubric to help you focus.
2. Read the required chapter(s) of the textbook and any additional recommended resources. Some answers may require you to do additional research on the Internet or in other reference sources. Choose your sources carefully.
3. Consider the course discussions so far and any insights gained from it.
4. Create your Assignment submission and be sure to cite your sources if needed, use APA style as required, and check your spelling.

Assignment:

For this week please complete the following two assignments:

1. Download the Module 7 Homework .docx. Compete all 20 homework questions for a total of 100 points. Please address all assigned questions using a different colored font. Include your name on the document before saving and submitting to the dropbox.
2. Download the Module 7 Homework.xlsx. You will use the excel file to complete the AVOVA and Chi-square calculations. Then upload the Excel file to the dropbox.

M7 Assignment UMBO – 4, 5

M7 Assignment PLG – 4

M7 Assignment CLO – 1, 2, 3, 4

Module 7 Homework

Please complete the following questions. Provide your answers in a different colored font to make them easily identifiable. Use the excel Module 7 Homework file to complete the calculations. Include your name on this answer sheet.

Problem 1

A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3

B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7

Answer the following question. For decimals, round to four decimal places.

1. State the null hypothesis for this test.

2. The grand mean for these observations is ____________

3. The SST for these observations is ____________

4. The SSA for these observations is ____________

5. The total degrees of freedom is _________________

6. The SSW is _________________

7. The within group mean square is _________________

8. The MSA is __________

9. At the 0.05 level of significance, the test statistic would be ________

10. The degrees of freedom are ________

11. Using α = 0.05, the critical value for this test would be ________

12. What is the p value _______

14. For the post hoc comparison you will have ____ pairwise comparisons.

15. The Bonferroni alpha is ______

16. Which pairs have a p value smaller than Bonferroni alpha? ______________

Problem 2

As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. Use α = 0.05

18. State the null hypothesis for the test:

19. State the alternative hypothesis:

20. The total degrees of freedom is _______

21. The amount of total variation or SST is __________.

22. The among group variation or SSA is __________.

23. The within group variation or SSW is __________.

24. The value of MSA is __________

25. The MSW is __________.

26. The degrees of freedom are ________

27. The null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the test statistic is greater than __________.

28. In testing the null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal, the value of the test statistic is __________.

29. What is your conclusion for this hypothesis test?

30. For the post hoc comparison you will have ____ pairwise comparisons.

31. The Bonferroni alpha is ______

32. Which pairs have a p value smaller than Bonferroni alpha? ______________

Problem 3

Four surgical procedures currently are used to install pacemakers. If the patient does not need to

return for follow-up surgery, the operation is called a “clear” operation. A heart center wants to

compare the proportion of clear operations for the 4 procedures. They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.

34. State the null hypothesis:

35. State the alternative hypothesis:

36. The test will involve _________ degrees of freedom.

37. The overall or mean proportion of clear operations is __________.

38. The expected cell frequency for the Procedure A/Clear cell is __________.

39. The expected cell frequency for the Procedure D/Return cell is __________.

40. The critical value of the test is ________.

41. The value of the test statistic is _________.

42. The p value is ______.

Problem 4

A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) parents’ educational status (College Degree or Non-College Degree) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table on problem 4 of the excel document.

44. Which test would be used to properly analyze the data in this experiment?

45. What would be the null hypothesis:

46. State the alternative hypothesis:

47. You will reject the H0 if _______________

48. The calculated test statistic is _____.

49. At 5% level of significance, the critical value of the test statistic is____

50. At 5% level of significance, there is sufficient evidence to conclude what?

Hypothesis Test Answer to question one The information that is needed to see whether there is an association between Gilbert being on duty and deaths is data table showing the number of deaths when Gilbert is on shift and when he is not on shift and the total number of patients in a shift. Answer to question two On the other hand, the deaths could have just occurred during Gilbert’s shift by coincidence or chance. Sometimes relationships of occurrences do not mean causation. Answer to question three The statistical test to be used in this case is chi-square test of association. This is because we are dealing with categorical data which is in form of a contingency table. Chi-square always tests for independence of occurrences. Answer to question three Hypothesis H0: There is no association between Gilbert’s presence and occurrence of patients’ deaths during his shift. H1: There is a significant association between Gilbert’s presence and occurrence of patients’ deaths during his shift. Alpha = 0.05

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