A Random Sample of 160 Car Purchases Are Selected and Categorized

Multiple Choice

A random sample of 160 car purchases are selected and categorized by age. 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 $\chi ^ { 2 }$ to test the claim that all ages have purchase rates proportional to their driving rates. Use $\alpha = 0.05$ .
$\begin{array}{l|cccc}\text { Age } & \text { Under 26 } & 26-45 & 46-65 & \text { Over } 65 \\\hline \text { Purchases } & 66 & 39 & 25 & 30\end{array}$

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