A company is studying three different safety programs, A, B, and C, in an attempt to reduce the number of work-hours lost because of accidents. Each program is to be tried at three of the company’s nine factories. The plan is to monitor the lost work-hours, y, for a 1-year period beginning 6 months after the new safety program is instituted.

a. Write a main effects model relating E(y) to the lost work-hours, x1, the year before the plan is instituted and to the type of program that is instituted.

b. In terms of the model parameters from part a, what hypothesis would you test to determine whether the mean work-hours lost differ for the three safety programs?

c. After the three safety programs have been in effect for 18 months, the complete main effects model is fit to the n = 9 data points. Using safety program A as the base level, the following results are obtained:

ŷ = -2.1 + .88x1 - 150x2 + 35x3
SSE = 1,527.27

Then the reduced model E(y) = β₀ + β₁x₁ is fit, with the result

ŷ = 15.3 + .84x₁     SSE  = 3,113.14

Test to determine whether the mean work-hours lost differ for the three programs. Use α = .05.