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# final.04 - Rep I Rep II Rep III Rep IV Rep V Block 1 Block...

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Final Exam 1. In a recycling experiment, six households were randomly selected. Each household was sep- arately assigned 5 randomly selected weeks for measuring its recycled materials. Each week, the weight of glass, tin, aluminum, plastic, and mixed paper was recorded. Construct a model and identify a design for this experiment. 2. Consider the model with factors Brick (B), Pumpkin(P), and Sun(S): Y ijk = μ + B i + P j ( B i ) + S k + BS ik + ± ijk , i = 1 , 2; k = 1 , 2 , 3; j = 1 , 2 , 3 ( i = 1); j = 1 , 2 ( i = 2) . (a) What is the form of PMM ( S k )? (b) Using the data below, is PMM ( S k ) estimable for all levels of k ? Verify. Brick Pumpkin Sun Y 1 1 1 16.0 1 1 2 19.8 1 1 3 . 1 2 1 14.4 1 2 2 14.2 1 2 3 . 1 3 1 9.4 1 3 2 8.8 1 3 3 . 2 1 1 10.1 2 1 2 12.7 2 1 3 15.4 2 2 1 14.4 2 2 2 12.6 2 2 3 13.5 3. Consider a 2 4 blocked full factorial design replicated 5 times. ABCD is confounded with Block in Rep I, ABC is confounded with Block in Rep II, ABD is confounded with Block in Rep III, ACD is confounded with Block in Rep IV, and BCD is confounded with Block in Rep V. The design appears below.

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Unformatted text preview: Rep I Rep II Rep III Rep IV Rep V Block 1 Block 2 Block 3 Block 4 Block 5 Block 6 Block 7 Block 8 Block 9 Block 10 (1) a (1) b (1) b (1) ab (1) b ab b ab a ab a b a a ab ac c d c c d ac c bc c ad d ac ad ad ac ad d bd d bc abc bc bd bd bc cd bc cd ac bd abd abd cd abc cd abc bd abc ad cd acd acd abc acd abd abd acd abd bcd abcd bcd bcd abcd bcd abcd bcd abcd acd abcd 1 (a) Block has 9 degrees of freedom. Account for the 9 degrees of freedom. (b) Paste the data on the webpage into the statistics package of your choice. If you include all 15 eﬀects and Block as a factor in your analysis model, you should have a model with 55 df for Error. Use the MSE from this model to test the (i) Interblock ABCD eﬀect, (ii) the Intrablock ABCD eﬀect, (iii) the Intrablock A eﬀect, (iv) The 4 df eﬀect for Rep. 2...
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final.04 - Rep I Rep II Rep III Rep IV Rep V Block 1 Block...

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