Midterm
1. Three different methods for measuring fuel injector flow are tested on three calibrated
master injectors by nine different operators (see table below).
Operator
Part 1 2 3 4 5 6 7 8 9
1 A=4.93 B=4.77 C=4.78 A=4.97 B=4.90 C=5.39 A=4.93 B=4.86 C=4.58
2 B=4.88 C=5.52 A=4.59 C=4.96 A=4.67 B=5.11 B=4.65 C=5.49 A=4.77
3 C=4.93 A=4.47 B=4.77 B=5.28 C=5.29 A=5.26 C=5.16 A=4.58 B=4.98
(a) Test a main effects model.
(b) Operators 1-3 work Shift 1, operators 4-6 work Shift 2, and operators 7-9 work
Shift 3. Test for a Shift effect.
(c) Include a Part by Method interaction in the main effects model. Is it significant?
Does it affect the significance of Method?
(d) Assume that the parts are tested in the order presented. Is the design balanced
for Residual Effects? Is Residual Effect significant? (Use the main effects model)
2. Biscuits are baked with 5 different levels of baking powder and relative rise is recorded
as the response. Results from a pilot study appear below:
Amount (tsp) .5 1 1.5 2 2 2.5
Relative Rise 8.3 12.7 20.6 28.3 29.5 29.8
(a) Test for the effect of amount of baking powder on relative rise using a cell means
model. Construct a linear contrast (use Table X) and test whether it is significant.
(b) Test for a linear effect of amount of baking powder on relative rise using a sim-
ple linear regression model. Compare your results (particularly the estimated
error) from the two methods. What are the advantages/disadvantages of the two
different estimates of error?
(c) If we wanted to detect a linear contrast of 4 with 90% power, how many repli-
cations would be needed? Compare your answer using the different estimates of
error from parts one and two. Assume α=.05.
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