An engineer is investigating the effects of four assembly methods (A, B, C, D) on the

assembly time of a color television component. Four operators are selected for the study.

Furthermore, the engineer knows that each assembly method produces such fatigue that

the time required for the last assembly may be greater than the time required for the first,

regardless of the method. That is, a trend develops in the required assembly time. To

account for this source of variability, the engineer uses the Latin square design shown below.

order of Operator

Assembly 1 2 3 4

1 C=10 D=14 A=7 B=8

2 B=7 C=18 D=11 A=8

3 A=5 B=10 C=11 D=9

4 D=10 A=10 B=12 C=14

a) Test if there is a difference between the four assembly methods. State the hypotheses and use = 5%.

b) Obtain the estimates of the treatment effects.

c) Use Tukey's method to perform pairwise comparisons by hand as well as SAS.

d) Check model assumptions.