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 ?= 0.005, 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. Age Gender16-24 25-34 35-44 45-54 55-64 65-74 75-84 85 and older Male 89 73 63 65 39 22 15 Female 45 34 30 20 17 1519 10 Are the proportions the same for each group? O A. No, the value of 2 is too low to conclude the proportions are the same. O B. Yes, the value of x2 is low enough to conclude the proportions are the same. O C. No, the value of x2 is too high to conclude the proportions are the same. O D. Yes, the value of y2 is high enough to conclude the proportions are the same.

Explanation / Answer

applying chi square test of Homogeneity

for above as p value is higher then 0.005 level

option B is correct

Observed OBS 16-24 25-34 34-44 45-54 55-64 65-74 75-84 85 and older Total male 89 73 63 65 39 22 15 12 378 female 45 34 30 20 17 15 19 10 190 Total 134 107 93 85 56 37 34 22 568 Expected Ei=?row*?column/?total 16-24 25-34 34-44 45-54 55-64 65-74 75-84 85 and older Total male 89.176 71.208 61.891 56.567 37.268 24.623 22.627 14.641 378 female 44.824 35.792 31.109 28.433 18.732 12.377 11.373 7.359 190 Total 134 107 93 85 56 37 34 22 568 chi square =(Oi-Ei)2/Ei 16-24 25-34 34-44 45-54 55-64 65-74 75-84 85 and older Total male 0.00 0.05 0.02 1.26 0.08 0.28 2.57 0.48 4.73 female 0.00 0.090 0.040 2.501 0.160 0.556 5.114 0.948 9.41 Total 0.00 0.13 0.06 3.76 0.24 0.84 7.69 1.42 14.139

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