Stat 4120 Take-Home Assignment 2 Solutions

Stat 4120 Take-Home Assignment 2 Solutions - Stat 4210...

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Stat 4210 Spring 2011 Take-Home Assignment 2 Solutions Answer all of the following questions clearly and completely. While I like to see SAS code and computer output when it is an important part of the answer, do not turn code or printout that you do not refer to. Be sure to perform the usual residual analysis. Each part of each question is worth three points and is graded according to the rubric contained in the syllabus. This assignment is due on Wednesday, February 23. 1: Do exercise 3.19 on page 69 of the textbook. Hint : Write out the Source of Variation and degrees of freedom portions of the ANOVA table and consider the precision of estimates of parameters. The partial ANOVA table for a 3x3 Latin Square design is Source df Treatment 2 Rows 2 Columns 2 Error 2 Total 8 There are only 2 degrees of freedom that can be used to estimate the residual variance. Consequently, the estimate will not be very precise. A solution is to replicate the experiment to create more degrees of freedom for estimating the residual variance. 2: Do exercise 3.20 on page 69 of the textbook. Source df SS MS F-value P-value Rows 5 150 150/5 = 30 30/5 = 6 0.0015 Columns 5 200 200/5 = 40 40/5 = 8 0.0003 Treatments 5 5 x 10 = 50 10 10/5 = 2 0.1225 Error 20 500 – (150+200+50) = 100 100/20 = 5 Total 35 500 In a 6x6 Latin Square, the Rows, Columns and Treatments each have 5 degrees of freedom. The total degrees of freedom value is 35 (6x6 – 1). Consequently, the Error degrees of freedom value is 20. Because the P-value for the Treatments is 0.1225, do not reject the null hypothesis of no treatment effect. In addition, the rather large F-values for Rows and Columns indicate that blocking was useful for both the Row and Column factors. Given numbers are shown in bold . The other calculations are indicated.
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3: Do exercise 3.25 on page 71 of the textbook. Notes : 1) In part (a), do not compare your result with the result of exercise 3.23. Do use a post hoc test, if appropriate, to decide which motor oil results in the best mean mileage. 2) To answer part (b) of the exercise, you do not have to do exercise 3.23. Just answer whether treating the drivers as a blocking variable turned out to be a good idea. a)
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Stat 4120 Take-Home Assignment 2 Solutions - Stat 4210...

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