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Homework12Solns

Homework12Solns - Stat 512 2 Solutions to Homework#12 Dr...

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Stat 512 – 2 Solutions to Homework #12 Dr. Simonsen Due Friday, December 2, 2005 by 4:30pm 1. KNNL 25.3: In each of the following cases, indicate whether ANOVA model I or model II is more appropriate and state your reasons: (a) In a study of absenteeism at a plant, the treatments are the three 8-hour shifts. There are only three shifts, and differences among these are of interest. Therefore a fixed effects model (I) is appropriate. (b) In a study of employee productivity, the treatments are 10 production employees selected at random from all production employees in a large company. These employees are selected at random to represent all employees. Therefore a random effects model (II) is appropriate. (c) In a study of anticipated annual income at retirement, the treatments are the four types of retirement plans available to employees. There are only four plans, and differences among these are of interest. Therefore a fixed effects model (I) is appropriate. (d) In a study of tire wear in 18-wheel trucks, the treatments are four tire locations selected at random. The four locations were selected at random to be representative of the entire tire, and are not of interest in themselves. Therefore a random effects model (II) is appropriate 2. KNNL 25.13: In a two-factor ANOVA study with a = 3, b = 2, and n = 5, the two factor effects are both random with σ 2 = 5.0, Assume that ANOVA model (24.39)) is applicable. 2 2 2 8.0, 10.0, and 6.0. α β αβ σ = σ = σ = (a) Obtain E{MSA}, E{MSB}, and E{MSAB} ( ) ( ) ( ) 2 2 2 2 2 2 2 2 5 2 5 8 5 6 5 3 5 10 5 6 5 5 6 E MSA bn n E MSB an n E MSAB n α αβ β αβ αβ = σ + σ + σ = + × × + × = = σ + σ + σ = + × × + × = = σ + σ = + × = 115 185 35 (b) What would be the expected mean squares if 2 0 αβ σ = , all other parameters remaining the same? ( ) ( ) ( ) 2 2 2 2 2 5 2 5 8 5 3 5 10 E MSA bn E MSB an E MSAB α β = σ + σ = + × × = = σ + σ = + × × = = σ = 85 155 5

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