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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 lower-order 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