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hw6sol - Stat 511 Homework 6 PMD solution Spring 2011 Note...

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Stat 511 Homework 6 PMD solution Spring 2011 Note: These are sketchy because I’m short of time and Yun has more important things to worry about. They give you a sense of my answers. I will return HW before the midterm if I get it from Yun. 1. The data in bacteria.txt are from a study of bacterial growth as a function of sugar concen- tration in the growth medium. This is a completely randomized design with five replicates of four sugar concentrations (1gm/ml, 2gm/ml, 3gm/ml, and 4gm/ml). The investigators want to know 1) whether sugar concentration affects bacterial growth and 2) does a simple model describe the relationship between sugar concentration and growth. Please analyze the data in an appropriate manner, using orthogonal polynomials, and briefly answer the investigator’s two questions. The orthogonal polynomial coefficients for four equally spaced groups are: X linear quadratic cubic 1 -3 1 -1 2 -1 -1 3 3 1 -1 -3 4 3 1 1 If you plot the data, or fit a model and look at a residual plot, you see quickly that the equal variance assumption is not appropriate. A plot of log variance vs log mean (a Box-Cox plot, from 500), indicates a log transformation is appropriate. So does looking at the residuals on the log scale. Working with Y = log grow , I get: 1) Yes, the 3 d.f. F statistic comparing the 3 sugar levels is 49.3, with a p-value of << 0.0001. Growth is fastest when sugar = 1 and declines with increasing sugar concentration.
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