Chapter 3.1, Problem 3.26ACA

Drug testing of firefighters. Hillsborough County Florida, has 42 fire stations that employ 980 career firefighters and 160 volunteers. Both types of firefighters are drug tested every six months. However the career firefighters and volunteers are treated as separate populations. For drug testing, 50% of the career firefighters are randomly selected and 50% of the volunteers are randomly selected. Some firefighters at a particular station argue that due to the smaller number of volunteers, an individual volunteer is more likely to be selected in the current sampling scheme than if all the career firefighters and volunteers were combined into a single population and 50% sampled. Do you agree? Explain your reasoning.

     $\left[H\mathrm{int}:\left(\begin{array}{c}N-1\\ n-1\end{array}\right)/\left(\begin{array}{c}N\\ n\end{array}\right)=n/N\right]$