11.73 To increase the motivation and productivity of workers, an electronics manufacturer decides to experiment with a new pay incentive structure at one of two plants. The experimental plan will be tried at plant A for six months, while workers at plant B will remain on the original pay plan.To evaluate the effectiveness of the new plan, the average assembly time for part of an electronic system was measured for employees at both plants at the beginning and end of the six-month period.

Suppose the following model was proposed:

Y = b0 + b1x1 + b2x2 + e where assembly time (hours) at end of sixmonth period assembly time (hours) at beginning of six-month period A sample of observations yielded where Test to see whether, after allowing for the effect of initial assembly time, plant A had a lower mean assembly time than plant B. Use .
[Note: When the (0, 1) coding is used to define a dummy variable, the coefficient of the variable represents the difference between the mean response at the two levels represented by the variable. Thus, the coefficient is the difference in mean assembly time between plant A and plant B at the end of the six-month period, and is the sample estimator of that difference.]