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 . Find the critical value $\chi \frac { 2 } { 0 }$ to test the claim that all ages have purchase rates proportional to their driving rates. Use $\alpha = 0.05$ .
$\begin{array} { l | c c c c } \text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over } 65 \\\hline \text { Purchases } & 66 & 39 & 25 & 30\end{array}$

A) 7.815
B) 6.251
C) 11.143
D) 9.348