The following table contains data from a study concerning the distribution of pa

Question

The following table contains data from a study concerning the distribution of party affiliation in a neighborhood. The interest was whether there was an association between registered political party and the race. Race Part Democrat Republican Independent 406 Total White Black Hispanic AsianTotal 431 390 180 159 164 503 896 902 828 190 95 106 82 282 2627 248 1227615 To determine whether there was an association between registered political party and the race, we would like to perform the Chi-square test. We first calculate the table of expected counts. Table below lists the The table is incomplete as results for four expected counts calculated cells in the lower-right corner of the table are removed and replaced by a, b, c, d respectively. Complete the table by calculating the values of a, b, c, d. Remember to show your calculation process. Race White Black Hispanic AsianTotal Part Democrat Republican Independent 386.75 193.81158.7388.92828 Total Ca 171.71 96.19896 172.96 96.89 902 1227 615 503 282 2627

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =12.592

since our test is right tailed,reject Ho when ^2 o > 12.592

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 16.332

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 4 - 1 ) = 2 * 3 = 6 is 12.592

we got | ^2| =16.332 & | ^2 | =12.592

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0.012

ANSWERS

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null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

test statistic: 16.332

critical value: 12.592

p-value:0.012

decision: reject Ho

X and Y are dependent, exists a association between them

MATRIX col1 col2 col3 col4 TOTALS row 1 431 190 180 95 896 row 2 390 248 159 105 902 row 3 406 177 164 82 829 TOTALS 1227 615 503 282 N = 2627

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