Question 3. [17 marks]

The quality control director for a clothing manufacturer wants to study the effect of operators and machines on the breaking strength (in pounds) of wool serge material. A batch of the material is cut into square yard pieces, and these are randomly assigned, 3 each, to all 12 combinations of 4 operators and 3 machines chosen specifically for the experiment. The results are provided below:

Operator I II III

A 115 111 109

A 115 108 110

A 119 114 107

B 117 105 110

B 114 102 113

B 114 106 114

C 109 100 103

C 110 103 102

C 106 101 105

D 112 105 108

D 115 107 111

D 111 107 110

a.[2] Use Minitab to produce output for this question. Insert your output here:

b.[3] At the 0.05 level of significance, is there an interaction between operator and machine? State the test statistic formula and value along with the p-value from your output. Draw your conclusions.

Test statistic:

p-value:

Conclusions:

c.[3] At the 0.05 level of significance, is there an effect due to operator? State the test statistic formula and value along with the p-value from your output. Draw your conclusions.

Test statistic:

p-value:

Conclusions:

d.[3] At the 0.05 level of significance, is there an effect due to machine? State the test statistic formula and value along with the p-value from your output. Draw your conclusions.

Test statistic:

p-value:

Conclusions:

e.[3] Use Minitab to create one line graph; plot the mean breaking strength for each operator for each machine. Comment on the results.

Graph:

Comments:

f.[3] Would a Post Hoc Test to examine differences between operators and differences between machines be appropriate? Explain. (Yes/no answers will receive a mark of zero.)