# 10_30_2ans - STAT 420 Examples for 10/30/2007 I I Fall 2007...

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STAT 420 Examples for 10/30/2007 Fall 2007 Contrast in the means μ 1 , μ 2 , … , μ I c 1 μ 1 + c 2 μ 2 + … + c I μ I = = I i i i c 1 where = I i i c 1 = 0 Scheffé’s multiple comparison : With 100 × ( 1 – γ )-percent confidence all contrasts in the I population means of the form = I i i i c 1 are bracketed by the bounds ( ) ( ) = = - - - ± I I i i i I I N I i i i n c s c F 1 2 pooled 1 1 , 1 Y ± where pooled s = MSE . 1. Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data ( μ g/g): Wheat 5.2 4.5 6.0 6.1 6.7 5.7 Barley 6.5 8.0 6.1 7.5 5.9 5.6 Maize 5.8 4.7 6.4 4.9 6.0 5.2 Oats 8.3 6.1 7.8 7.0 5.6 7.2 n i i y s i s i 2 Wheat 6 5.7 0.7668 0.588 Barley 6 6.6 0.9508 0.904 Maize 6 5.5 0.6693 0.448 Oats 6 7.0 1.0139 1.028 Source SS DF MS F Treatment 9.24 3 3.08 4.151 Error 14.84 20 0.742 Total 24.08 23 F 0.05 ( 3, 20 ) = 3.10 t 0.025 ( 20 ) = 2.086

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a) Construct a 95% confidence interval for the difference between the average thiamin content for Oats and Maize. pooled s = MSE has N I = 20 degrees of freedom associated with it.
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## This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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10_30_2ans - STAT 420 Examples for 10/30/2007 I I Fall 2007...

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