hw12 - STATISTICS 500 Fall 2009 Homework 12, corrected on...

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Unformatted text preview: STATISTICS 500 Fall 2009 Homework 12, corrected on campus Friday, 11 Dec 2009, in lecture (11 am) or by e-mailto Chuanlong, dclong@iastate.edu, no later than noon. off campus Monday, 14 Dec 2009, by 4 pm to Nicole Rembert, email: rembeall@iastate.edu or FAX: 515-294-4040 (please include cover page with Stat 500 / Nicole Rembert). 1. Nested designs A production engineer is studying the effects of machine model (factor A) and machine (factor B) on the output in a pop (soda, outside the Midwest) bottling plant. The study compared three models of bottling machine, using four machines of each model. We can imagine that model is randomly assigned to the machine. The production of each machine ((# cases produced per day) was recorded on five successive days. There are five responses for each machine. The data are given below and in bottle.txt on the class web site. Bottle.tex contains the data in a condensed format with one line per model and machine with 5 values (one per day) on the line. To analyze the data, you need to create one line per day (a total of 60 observations). Model i : 1 2 3 Machine j : 1 2 3 4 1 2 3 4 1 2 3 4 Day k = 1: 65 68 56 45 74 69 52 73 69 63 81 67 k = 2: 58 62 65 56 81 76 56 78 83 70 72 79 k = 3: 63 75 58 54 76 80 62 83 74 72 73 73 k = 4: 57 64 70 48 80 78 58 75 78 68 76 77 k = 5: 66 70 64 60 68 73 51 76 80 75 70 71 (a) You are most interested in comparing the mean performance of the three models of bottling machine. A student analyzes the data and shows you the following ANOVA table and F test of Ho: 1 = 2 = 3 : Source d.f. MS F p-value model 2 847.82 14.2 < 0.0001 error 57 59.74 c.total 59 You ask the student if this is the correct analysis and he tells you, Yes, because there are no blocks in the design. Do you agree? If this isnt the correct analysis, what would be a more appropriate analysis? (b) Using an appropriate model for the analysis, estimate the difference between models 1 and 2, calculate the s.e. of that difference and test whether that difference equals 0. 2. Design of a microarray experiment The following problem is motivated by a recent microarray experiment. Fungal infections of crop plants are a common problem in the midwest where the summers are warm and humid. There is often some genetic control of which fungi infect which crop plants. This is a study of 2 genetic isolates of one fungus species (A and B)infect which crop plants....
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This note was uploaded on 02/11/2012 for the course STAT 500 taught by Professor Staff during the Fall '08 term at Iowa State.

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hw12 - STATISTICS 500 Fall 2009 Homework 12, corrected on...

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