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Unformatted text preview: Midterm 1. Three diﬀerent methods for measuring fuel injector ﬂow are tested on three calibrated master injectors by nine diﬀerent operators (see table below). Part 1 2 3 1 A=4.93 B=4.88 C=4.93 2 B=4.77 C=5.52 A=4.47 3 C=4.78 A=4.59 B=4.77 4 A=4.97 C=4.96 B=5.28 Operator 5 6 B=4.90 C=5.39 A=4.67 B=5.11 C=5.29 A=5.26 7 A=4.93 B=4.65 C=5.16 8 B=4.86 C=5.49 A=4.58 9 C=4.58 A=4.77 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) Relative Rise .5 8.3 1 12.7 1.5 20.6 2 28.3 2 29.5 2.5 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 simple 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 replications would be needed? Compare your answer using the diﬀerent estimates of error from parts one and two. Assume α = .05. 1 ...
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This note was uploaded on 10/01/2009 for the course STAT stat706 taught by Professor Johnm.grego during the Spring '08 term at South Carolina.
- Spring '08