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Multiple choice questions from Analysis of Variance

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An operations analyst collected data on the number of acceptable units produced from equal amounts of raw material by 24 entry-level piece work employees who had received special training.Four training levels were used (6, 8, 10, and 12 hours) with 6 employees randomly assigned to each level. The resulting means and ANOVA table were obtained:

Treatment 6 8 10 12
Mean (¯xi?) 62 72 85 86

Source SS df MS

Treatment 2356.5 3 785.5
Error 2014.9 20 100.74
Total 4371.4 23

Answer the next 5 questions based on these data.

[1] The experimental design used for this experiment and the reason for using it are

a) the completely randomized design since the experimental units are homogeneous.
b) the randomized complete block design since the experimental units are homogeneous.
c) the completely randomized design to control for the variation in employees.
d) the randomized complete block design to control for the variation of employees.
e) a 4 × 6 factorial experiment since we wish to study the effects of both training levels and employees.

[2] What is the f-value for the above ANOVA?
a) 1.17
b) 23.39
c) 0.13
d) 6.67
e) 7.80
[3] What is the rejection region for the above ANOVA? That is, if f ¸ F.05, v1, v2 we reject H0. What is F.05, v1, v2?
a) 2.78
b) 2.87
c) 3.03
d) 3.10
e) 3.49

[4] A comparison that would compare the mean production of workers with shorter training (6 or 8 hours) to those with longer training (10 or 12 hours) is
a) ` = &#956;6 &#8722; &#956;8
b) ` = &#956;10 &#8722; &#956;12
c) ` = 3&#956;6 &#8722; &#956;8 &#8722; &#956;10 &#8722; &#956;12
d) ` = &#956;6 &#8722; &#956;8 + &#956;10 &#8722; &#956;12
e) ` = &#956;6 + &#956;8 &#8722; &#956;10 &#8722; &#956;12

[5] The calculated value of Tukey's W at level 0.05 is 16.23. The significant differences in mean production levels found by using Tukey's method are

a) &#956;6 not equal to &#956;12
b) &#956;6 not equal to &#956;10, &#956;6 not equal to &#956;12
c) &#956;6 not equal to &#956;10, &#956;6 not equal to &#956;12, &#956;8 not equal to &#956;12
d) &#956;6 not equal to &#956;10, &#956;6 not equal to &#956;12, &#956;8 not equal to &#956;10, &#956;8 not equal to &#956;12
e) &#956;6 not equal to &#956;8, &#956;6 not equal to &#956;10, &#956;6 not equal to &#956;12, &#956;8 6 not equal to &#956;10, &#956;8 not equal to &#956;12
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