# 11_07_11ans - thought inflation of unemployment was a more...

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STAT 409 Examples for 11/07/2011 Fall 2011 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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2. In a random sample of 500 voters, each individual was asked whether he or she
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Unformatted text preview: thought inflation of unemployment was a more serious problem. The individuals were also classified by party affiliation. The results were as follows: Party Unemployment Inflation Democrat 150 70 Republican 100 80 Other 60 40 Use a 5% level of significance and test whether political party affiliation and perceived problem are independent. H : political party affiliation and perceived problem are independent. H A : Not H ( political party affiliation and perceived problem are not independent ). Party Unemployment Inflation Democrat 150 70 220 136.4 83.6 1.356012 2.212440 Republican 100 80 180 111.6 68.4 1.205735 1.967251 Other 60 40 100 62 38 0.064516 0.105263 310 190 500 Q = 6.911217 . ( 3 1 ) ( 2 1 ) = 2 degrees of freedom. 2 05 . = 5.991 . Q = 6.911217 > 5.991 = 2 . Reject H ....
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## This note was uploaded on 11/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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11_07_11ans - thought inflation of unemployment was a more...

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