5. (37 points) A manager wishes to determine whether the mean times required to complete a certain task differ for the t

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5 37 Points A Manager Wishes To Determine Whether The Mean Times Required To Complete A Certain Task Differ For The T 1 (42.65 KiB) Viewed 87 times

5. (37 points) A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 5 employees with each of the three levels of training (Beginner, Intermediate and Advanced). The data is summarized in the table. Level of Training n y. Advanced 5 24.4 Intermediate 27.0 5 Beginner 5 32.6 The analysis of variance is given as follows: Source DF MS F p-value Treatment 2 150.100 75.050 7.442 0.0079 12 14 Error 121.012 10.084 Total 271.112 (a) (4 points) Write a linear contrast for the question: Is the mean time required to complete a certain task for the advanced level of training different than the mean time required for the intermediate level of training? (b) (4 points) Write a linear contrast for the question: Is the mean time required to complete a certain task for the advance level of training different than the average of the mean times required for the other two levels of training? (a (9 points) Are the two contrasts defined in (a) and (b) mutually orthogonal? Explain why or why not (d) (20 points) Use Scheffe's 5 procedure to determine if the linear contrasts defined in (b) is significantly different from zero. Use a = 0.05. (Show all the necessary details)