423sp06exam2soln

423sp06exam2soln - Math/Stat 423/523 Exam 2 Spring 2006...

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Math/Stat 423/523 Spring 2006 Solution Key Exam 2 1. An experiment was carried out to study the effects of factors A, B and C. The ANOVA table and interaction plot are given below. Source DF SS MS F P A 1 17.36 17.36 31.31 0.000 B 2 21.86 10.93 19.71 0.000 C 2 8.37 4.19 7.55 0.004 A*B 2 1.06 0.53 0.96 0.406 A*C 2 3.20 1.60 2.91 0.082 B*C 4 6.51 1.63 2.94 0.050 A*B*C 4 2.08 0.52 0.94 0.463 Error 18 9.98 0.55 Total 35 70.42 The full model fit to data is: X ijkl = μ + α i + β j + χ k + γ ij AB + γ ik AC + γ jk BC + γ ijk ABC + ε ijkl a. Fill in the missing entries in the ANOVA table. [6 pts] b. Test the hypothesis H 0 : { γ ik AC =0 for all i, k} versus H a : {H 0 is false} at the α =.05 level. [7 pts] Test Statistic = ___f=2.91___ Reject Region = ___{f > F .05,2,18 = 3.55}__ Circle one: Retain c. Compute the value of R 2 in this analysis . Does this number suggest a good fit of the model to the data? Explain briefly. [6 pts] % 8 . 85 42 . 70 98 . 9 1 R 2 = - = This is a high R 2 that indicates a good fit of the model to the data. d. Based on the numerical results, what smaller model may adequately describe the data? Give a one-sentence explanation for your answer . [6 pts] X ijkl = μ + α i + β j + χ k + γ jk BC + ε ijkl Factors A, B, C, and the interaction between B and C are judged significant at the .05 level.
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2. An experiment was performed to determine the effect of four different chemicals on the strength of a fabric. Five fabric samples were randomly selected, and a completely randomized block design (block = {fabric sample}) was run by testing
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423sp06exam2soln - Math/Stat 423/523 Exam 2 Spring 2006...

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