The contingency table below shows the results of a random sample of motor vehicl

Question

The contingency table below shows the results of a random sample of motor vehicle crash deaths by age and gender. At alpha = 0.10, perform a homogeneity of proportions test on the claim that the proportions of motor vehicle crash deaths involving males or females are the same for each group. Are the proportions the same for each group? A. Yes, the value of X^2 is low enough to conclude the proportions are the same B. No, the value of X^2 is too low to conclude the proportions are the same C. Yes, the value of X^2 is high enough to conclude the proportions are the same. D. No, the value of X^2 is too high to conclude the proportions are the same.

Explanation / Answer

for 7 degree of freedom critical value at 0.1 level =12.017

test stat =10.7545

as test stat is less then critical value we can not reject null hypothesis that both have equal proportion

hence optionA is correct

Observed O 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Total male 88 80 60 57 30 26 20 7 368 female 44 25 22 26 20 15 11 9 172 Total 132 105 82 83 50 41 31 16 540 Expected E=rowtotal*column total/grand total 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Total male 89.956 71.556 55.881 56.563 34.074 27.941 21.126 10.904 368 female 42.044 33.444 26.119 26.437 15.926 13.059 9.874 5.096 172 Total 132 105 82 83 50 41 31 16 540 chi square =(O-E)^2/E 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Total male 0.043 0.9965 0.3035 0.0034 0.4871 0.1348 0.0600 1.3976 3.425 female 0.091 2.132 0.649 0.007 1.042 0.288 0.128 2.990 7.329 Total 0.133 3.129 0.953 0.011 1.529 0.423 0.188 4.388 10.7545

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