A Random Sample of 160 Car Purchases Are Selected and Categorized

question 18

Essay

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 .
$\begin{array} { l | c c c c } \text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over } 65 \\\hline \text { Purchases } & 66 & 39 & 25 & 30\end{array}$

---

Definitions:

Standard of Proof

The level of evidence necessary to prove a legal claim or charge, varying by legal context, such as "beyond a reasonable doubt" in criminal cases or "preponderance of the evidence" in civil cases.

Clear and Convincing

A standard of evidence requiring a high level of certainty to establish a fact in legal proceedings, higher than the preponderance of evidence but lower than beyond a reasonable doubt.

Beyond a Reasonable Doubt

The highest standard of proof required in a criminal case, indicating that there is no plausible reason to believe otherwise than the defendant is guilty.

Circuit Courts

Courts that have appellate jurisdiction and cover a particular geographical area in the United States, also hearing a wide range of civil and criminal cases at the federal level.