A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. 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 . Calculate the chi-square test statistic $\chi ^ { 2 }$ used to test the claim that all ages have crash rates proportional to their driving rates.

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

A) 75.101
B) 85.123
C) 101.324
D) 95.431

Question

A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. 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 . Calculate the chi-square test statistic

\chi ^ { 2 }

used to test the claim that all ages have crash rates proportional to their driving rates.

\begin{array}{l|cccc}\text { Age } & \text { Under 26 } & 26-45 & 46-65 & \text { Over 65 } \\\hline \text { Drivers } & 66 & 39 & 25 & 30\end{array}

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

A) 75.101
B) 85.123
C) 101.324
D) 95.431

Quizplus · Accepted Answer

The chi-square test statistic is calculated by comparing the observed frequencies with the expected frequencies, which are based on the given age distribution percentages. The expected frequencies are calculated as follows: Under 26: $160 \times 0.18 = 28.8$, 26-45: $160 \times 0.39 = 62.4$, 46-65: $160 \times 0.31 = 49.6$, Over 65: $160 \times 0.12 = 19.2$. The chi-square statistic is then calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency for each category. Calculating this gives a chi-square statistic of approximately 75.101.

A Random Sample of 160 Car Accidents Are Selected and Categorized