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# ass 4 - STAT 3504 Assignment 4 DUE Monday March 22 1 In a...

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STAT 3504 Assignment 4 DUE: Monday March 22 1. In a study of length of hospital stay (in number of days) of persons in 4 income groups, the parameters are as follows: μ 1 = 5.1, μ 2 = 7.9, μ 3 = 7.9, μ 4 = 9.5, σ = 2.8 Assume single fixed factor levels ANOVA model I is appropriate. What are the values of the τ i if the ANOVA model is expressed in the factor effects formulation with r = i r 1 = i . μ μ ? 2. A study was carried out to compare 3 different display panels for use by air traffic controllers. Each display was tested in a simulated emergency condition. 12 highly trained air traffic controllers took part in the study. 4 controllers were randomly assigned to each display panel. The time (in seconds) to stabilize the emergency condition was recorded. The results are given below. Display Panel A 21 27 24 26 B 24 21 18 19 C 40 36 35 32 a) Use PROC ANOVA in SAS to find the ANOVA table and the fitted means for each display panel (remember the MEANS statement). State the null and alternative hypotheses for testing whether the true mean stabilization times differ for the 3 display panels. b) Define indicator (dummy) variables for a regression approach to the analysis of variance in such a way that the regression coefficients of these variables are the factor level effects τ i . Give the regression model. c) Set up the Y , X , and β matrices. d) Use SAS to obtain the fitted regression equation (and Anova table). e) Express Y , Y , Y 3. 2. 1. (obtained in part (a)) in terms of the β ˆ 's of the regression equation. f) Set up the null and alternative hypotheses for testing for inequality of the true mean stabilization times. g) Why is the hypothesis test in part (f) equivalent to the hypothesis test of part (a)? 3. The Marketing Department of a large supermarket chain is interested in whether the number of packages of disposable razors sold in a week differs for 4 different price levels. 5 stores are

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