A Random Sample of 160 Car Purchases Are Selected and Categorized

question 26

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 $\chi _ { 0 } ^ { 2 }$ 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) \(9.348\)

---

Definitions:

Reconquesta

The period in the history of the Iberian Peninsula, spanning several centuries, during which Christian kingdoms gradually reconquered territory from the Muslim Moors who had invaded in the 8th century.

Columbian Exchange

The extensive exchange of flora, fauna, cultural practices, human groups, technological advancements, ailments, and concepts between the Americas and the Old World after Columbus's expeditions.

Tainos

Indigenous people of the Caribbean who were the first Native Americans to encounter Columbus upon his arrival to the New World.

Tenochtitlan

The capital city of the Aztec Empire, located on an island in Lake Texcoco in present-day Mexico City, known for its complex architecture and significant cultural and religious importance.