11.50 An insurance company is experimenting with three different training programs, A, B, and C, for its salespeople. The following main effects model is proposed:

where Y  monthly sales (in thousands of dollars)

x1  number of months of experience Training program A is the base level.

a What hypothesis would you test to determine whether the mean monthly sales differ for salespeople trained by the three programs?

b After experimenting with 50 salespeople over a 5-year period, the complete model is fit, with the result SSE  140.5 Then the reduced model is fit to the same data, with the result SSE  183.2 Test the hypothesis you formulated in part (a).

Use a  0.05.

yN = 11.4 + 0.4x1 E(Y ) = b0 + b1x1 yN = 10 + 0.5x1 + 1.2x2 - 0.4x3 x3 = e 1 if training program C was used 0 otherwise x2 = e 1 if training program B was used 0 otherwise E(Y) = b0 + b1x1 + b2x2 + b3x3 b1 = b2 = 0 Y = b0 + b1x1 + b2x2 + b3x3 + b4x4 + e