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 $\chi _ { 0 } ^ { 2 }$ 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) $7.815$
B) $6.251$
C) $11.143$
D) $9.348$

Question

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 $\chi _ { 0 } ^ { 2 }$ 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) $7.815$
B) $6.251$
C) $11.143$
D) $9.348$

Quizplus · Accepted Answer

The degrees of freedom for this chi-square test are calculated as the number of categories minus one, which is $4 - 1 = 3$. For a significance level of $\alpha = 0.05$ and $3$ degrees of freedom, the critical value $\chi^2$ is $7.815$.

A Random Sample of 160 Car Purchases Are Selected and Categorized