The crosstabulation below comes from the Homicide 2005 data set. Does there seem

Question

The crosstabulation below comes from the Homicide 2005 data set. Does there seem to be a relationship between gender of homicide victim and borough where they were killed? Answer yes or no and explain how you know. This answer has not been graded yet.

Summa Cases Missing Valid Total N Percent N Percent N Percent 0.0% 540 100.0% Borough * Recoded gender 540 | 100.0% Borough * Recoded gender [count, column 90] Total 0 Recoded gender Female Borough Male Bronx Brooklyn New York Queens Staten Island Total 101.00 22.90% 181.00 41.04% 72.00 16.33% 76.00 17.23% 11.00 2.49% 441.00 100.00% 28.00129.00 28.28%| 23.89% 30.00211.00 30.30% 39.07% 91.00 19.19% 16.85% 94.00 18.18% 17.41 % 15.00 4.04% 2.78% 99.00540.00 100.00% 100.00% 19.00 18.00 4.00

Explanation / Answer

We shall do chi-square test to know relationship between gender and borough where they are killed.

H0 : there is no relationship between gender and borough where they are killed.

Ha : There is significant relationsip between  gender and borough where they are killed.

So observed contigency table (5 x 2)

Expected value Table

Expected value is calcualted

i.e. For bronx and Male = (Total bronx people) * (Total male)/ Total people = 441 * 129/540 = 105.35

Chi -square Table

X2 = (O - E)2/E

Here

X2 = 4.498

where dF = (5 -1) * (2-1) = 4 and alpha = 0.05

so X2critical = 9.488

p - value = 0.3428

so here X2 < X2critical so we fail to reject the null hypothesis and conclude that there is no significant relationship between gender and borough they are murdered.

Gender Borough male Female Total Bronx 101 28 129 Brooklyn 181 30 211 Newyork 72 19 91 Queens 76 18 94 Staten Is 11 4 15 Total 441 99 540

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