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Refer to given Exercise. Consider the following two contrasts of totals: (1) difference between the totals for training programs 1 and 3; (2) difference between the totals for the sum of training programs 1 and 3 and twice that of training program 2.
(a) Find the sum of squares due to each of these two contrasts.
(b) What null hypothesis is indicated by contrast 2? Test the hypothesis at a level of significance of 0.05 and explain your conclusions.
Exercise Three training programs are being considered for auditors in an accounting firm. The success of the training programs is measured on a rating scale from 0 to 100, with higher values indicating a desirable program. The company has categorized its auditors into three groups, depending on their number of years of experience. Three auditors are selected from each group and are randomly assigned to the training programs. Table shows the ratings assigned to the auditors after they completed the training program.
(a) Is there a difference in the training programs as indicated by the mean evaluation scores? Test at the 10% level of significance.
(b) Find a 90% confidence interval for the difference in the mean evaluation scores of training programs 1 and 3. Is there a difference between these two programs?
Years of Experience
Training Program
1
2
3
0-5
70
65
81
5-10
75
80
87
10-15
82
94
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