A Random Sample of 160 Car Accidents Are Selected and Categorized

Multiple Choice

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 $\chi ^ { 2 }$ used to test the claim that all ages have crash rates proportional to their driving rates.
$\begin{array}{l|cccc}\text { Age } & \text { Under 26 } & 26-45 & 46-65 & \text { Over } 65 \\\hline \text { Drivers } & 66 & 39 & 25 & 30\end{array}$

A) $85.123$
B) $95.431$
C) $75.101$
D) $101.324$