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Unformatted text preview: Midterm 1. In a Complete Randomized Design, 7 diﬀerent levels of baking powder were tested for their eﬀect on relative rise of biscuit dough. 4 biscuits were baked using each recipe. Use α = .05 for all tests. (a) Test the cell means model and examine the residuals. Are model assumptions satisﬁed? (b) Test for a linear trend against the intercept model. (c) Test all orthogonal polynomial models for lack of ﬁt against the cell means model (be sure to include lowerorder polynomial terms in each of these models). Which models are adequate? 0 tsp 3.1 2.3 1.9 2.7 .25 tsp 11.4 11.0 11.3 9.5 .5 tsp 27.8 29.2 26.8 26.0 .75 tsp 47.6 47.0 47.3 45.5 1 tsp 61.6 62.4 63.0 63.9 1.25 tsp 63.6 65.2 61.5 63.3 1.5 tsp 64.2 64.8 64.4 66.1 2. A Quality Control department at an adhesive company tests three types of backing using three diﬀerent tests. As the QC department has only 3 technicians, a simple latin square design was proposed as a pilot study. A single roll of tape constitutes an experimental unit. Use α = .05 as your test size. (a) Analyze the design. Are treatment eﬀects signiﬁcant? (b) Test Ho : µB − µA = 0. (c) The experiment is easily replicated with other rolls of tape. Using the same technicians and tests, the experiment was replicated 10 times. What alternative values of L = µB − µA can we detect in this experiment with 90% power? Use the MSE estimate from the pilot study as your estimate of σ 2 . Tech 1 2 3 1 A=2.7 B=3.1 C=2.5 Test 2 C=10.6 A=10.8 B=10.7 3 B=.5 C=.2 A=.5 3. Analysis of a Balanced Incomplete Block Design with b=a=5, k=r=4 generated the ANOVA table below. (a) (b) (c) (d) Complete the table What is σβ ? ˆ2 Compute V (ˆ), V (˜) and π. τ τ 2 τ τ When σβ = 0, derive a general formula for the ratio V (ˆ)/V (˜). What implicaˆ tions do you think this has for π? Source Treatment Block(Adjusted) Error Total df SS 241 41 215 497 MS 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
 JohnM.Grego

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