Mr. Elek Trico, an industrial engineer, is investigating the effect of four assembly methods (A, B, C, D) on the assembly time for a color television component. Four operators are selected for the study. Furthermore, Mr. Elek Trico knows that each test assembly method (1, 2, 3, 4) 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. Mr. Elek Trico also suspects that the workplace (a, B, Y, 8) used by the four operators may represent an additional source of variation. Analyze the data from this experiment.

OPERATOR
ORDER OF ASSEMBLY 1 2 3 4
1 Cβ = 14 Bγ = 7 Dδ = 14 Aα = 8
2 Bα = 6 Cδ = 14 Aγ = 10 Dβ = 10
3 Aδ = 9 Dα = 11 Bβ = 6 Cγ = 17
4 Dγ = 9 Aβ = 8 Cα = 19 Bδ = 5

a. Find the residuals for all observations