Question

Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below. 

\[ \begin{array}{|c|c|c|c|} \hline \text{Injured} & \text{Non-injured} & \text{Total workers} \\ \hline \text{Roof-bolter operators} & 13 & 12 & 25 \\ \text{Loader operators} & 35 & 72 & 107 \\ \hline \text{Total workers} & 48 & 84 & 132 \\ \hline \end{array} \] The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)

Hint:

The odds ratio compares the odds of an event occurring in two different groups.

Answer 1

Correct Answer: 2.2 - 2.3

The odds ratio is given by:
\[ \text{Odds ratio} = \frac{\text{Odds for roof-bolter operators}}{\text{Odds for loader operators}} \] Odds for roof-bolter operators:
\[ \text{Odds}_{\text{roof-bolter}} = \frac{13}{12} = 1.083 \] Odds for loader operators:
\[ \text{Odds}_{\text{loader}} = \frac{35}{72} = 0.486 \] Thus, the odds ratio is:
\[ \text{Odds ratio} = \frac{1.083}{0.486} = 2.23 \] Thus, the odds ratio is \( \boxed{2.23} \).