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 = 0.05, 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. No, the value of X^2 is low to conclude the proportions are the same B. No, the value of X^2 is too high to conclude the proportions are the same C. Yes, the value of X^2 is low enough to conclude the proportions are the same. D. Yes, the value of X^2 is high enough to conclude the proportions are the same.

Explanation / Answer

at 7 degree if freedom and 0.05 level ; critical value =12.017

applying chi square test:

as test stat 17.8552 is greater then critical value we reject null hypothesis

option B is correct

Observed O 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Total male 91 70 64 58 32 21 16 9 361 female 41 34 25 24 25 17 20 11 197 Total 132 104 89 82 57 38 36 20 558 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 85.398 67.283 57.579 53.050 36.876 24.584 23.290 12.939 361 female 46.602 36.717 31.421 28.950 20.124 13.416 12.710 7.061 197 Total 132 104 89 82 57 38 36 20 558 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 0.368 0.1097 0.7161 0.4618 0.6448 0.5226 2.2820 1.1992 6.304 female 0.673 0.201 1.312 0.846 1.182 0.958 4.182 2.197 11.551 Total 1.041 0.311 2.028 1.308 1.826 1.480 6.464 3.397 17.8552

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