# 11_13_09ans - STAT 409 1 Fall 2009 Examples for A group of...

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STAT 409 Examples for 11/13/2009 Fall 2009 1. A group of 500 children (250 boys and 250 girls) were asked to identify their favorite color. We obtain the following data: Favorite Color Sex Yellow Red Blue Brown Boys 107 85 33 25 Girls 93 65 67 25 A toy manufacturer wants to know if the color preferences of boys and girls differ. Perform χ 2 test of homogeneity using a 1% level of significance. H 0 : In all 4 response categories (Yellow, Red, Blue, Brown), the probabilities are equal for these 2 populations (Boys, Girls). H A : Not H 0 . Favorite Color Sex Yellow Red Blue Brown Total Boys 107 85 33 25 250 100 75 50 25 0.49 1.33333 5.78 0 Girls 93 65 67 25 250 100 75 50 25 0.49 1.33333 5.78 0 Total 200 150 100 50 500 Q = 15.20667 . ( 2 – 1 ) ( 4 – 1 ) = 3 degrees of freedom. 2 01 . 0 χ = 11.34 . Q = 15.20667 > 11.34 = 2 α χ . Reject H 0 .

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1 ½ . Observed frequencies: Blood Type O A B AB Town X 130 75 70 25 300 Town Y 100 45 30 25 200 230 120 100 50 500 H 0 : p XO = p YO , p XA = p YA , p XB
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## This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.

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11_13_09ans - STAT 409 1 Fall 2009 Examples for A group of...

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