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 = 0.025, 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 too low to conclude the proportions are the same. B. Yes. the value of x^2 is high enough 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. No. the value of x^2 is too high to conclude the proportions are the same.

Explanation / Answer

here degree of freedom =(row-1)*(column-1) =(2-1)*(8-1)=7

for 7 degrees of freedom and 0.025 level ; critical value =16.013

as above test stat 12.216 is lower then critical value.

therefore option C is correct.

Observed O 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 or older Total male 86 75 69 58 31 29 21 8 377 female 45 25 30 23 17 14 19 10 183 Total 131 100 99 81 48 43 40 18 560 Expected E=rowtotal*column total/grand total 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 or older Total male 88.191 67.321 66.648 54.530 32.314 28.948 26.929 12.118 377 female 42.809 32.679 32.352 26.470 15.686 14.052 13.071 5.882 183 Total 131 100 99 81 48 43 40 18 560 chi square =(O-E)^2/E 16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 or older Total male 0.054 0.8758 0.0830 0.2208 0.0535 0.0001 1.3052 1.3993 3.992 female 0.112 1.804 0.171 0.455 0.110 0.000 2.689 2.883 8.224 Total 0.167 2.680 0.254 0.676 0.164 0.000 3.994 4.282 12.216

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