A random sample of 160 car accidents are selected and categorized by the age of
ID: 3154581 • Letter: A
Question
A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic used to test the claim that all ages have crash rates proportional to their driving rates.
Age >26 26-45 46-65 45<
Drivers 66 39 25 30
A) 95.431
B)101.324
C)85.123
D)75.101
Explanation / Answer
The following table is obtained:
From the above calcuations
chi-square test statistic = 75.101
Answer : Option ( D )
Categories Observed Expected (fo-fe)2/fe Category 1 66 160*0.18=28.8 (66-28.8)2/28.8 = 48.05 Category 2 39 160*0.39=62.4 (39-62.4)2/62.4 = 8.775 Category 3 25 160*0.31=49.6 (25-49.6)2/49.6 = 12.201 Category 4 30 160*0.12=19.2 (30-19.2)2/19.2 = 6.075 Sum = 160 160 75.101
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