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 46-65 group, and 12 % for the group over 65 . Test the claim that all ages have purchase rates proportional to their driving rates. Use α=0.05 .
$\begin{array} { l | c c c c }
\text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over } 65 \
\hline \text { Purchases } & 66 & 39 & 25 & 30
\end{array}$

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  46-65  group, and  12 %  for the group over 65 . Test the claim that all ages have purchase rates proportional to their driving rates. Use  α=0.05 .
$\begin{array} { l | c c c c } 
\text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over } 65 \
\hline \text { Purchases } & 66 & 39 & 25 & 30
\end{array}$

Quizplus · Accepted Answer

The Answer is critical value

imes \frac { 2 } { 0 }

=7.815 ; chi-square test statistic

x ^ { 2 }

=75.101 ; reject H₀ ; There is sufficient evidence to reject the claim that all ages have the same purchase rate.

A Random Sample of 160 Car Purchases Are Selected and Categorized