# hw5 - STAT424 Spring 2010 Homework#5 Apr 1 2010 Homework 5...

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Unformatted text preview: STAT424 Spring 2010 Homework #5 Apr 1, 2010 Homework 5 Due: Thursday, Apr 8, 2010 1) A child whose mother drank too much alcohol while pregnant with the child can show symptoms of fetal alcohol syndrome , which includes being more impulsive than normal, thereby having trouble learning. An experiment was carried out on n = 20 rats. They were divided into two groups based on age (younger and older) and two groups based on whether their mothers drank alcohol or not. Each rat then had to learn a task. The y ijk ’s are the number of trials until they learned. (The lower, the better.) The design was balanced, so there were N = 5 observations per cell. The data are summarized as follows. Age ↓ ; Alcohol → No Yes Younger 4.2 16.4 Older 6.0 6.4 1. Compute the LS estimate for the saturated model for the four cells. 2. Compute the LS estimate for the additive model for the four cells. 3. Fill in all the blanks in the ANOVA table below. (There are 16 blanks to fill.) Source SS (sum of squares) df MS = SS/df F Age Alcohol Interaction Error 75.6 —— Total —— —— 4. Find k ˆ y C · k 2 and k ˆ y ( R + C ) · C k 2 . 5. Do the F tests. Does the additive model fit? What is the best model? 2) Analyzing the following two-way ANOVA model (unbalanced design). The data are sum- marized as follows ¯ y ij · j 1 2 3 i 1 2.03 3.18 2.31 2 1.57 3.57 1.90 n ij j 1 2 3 i 1 5 3 2 2 7 3 5 Also X i X j X k ( y ijk...
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hw5 - STAT424 Spring 2010 Homework#5 Apr 1 2010 Homework 5...

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