EXAMPLE 3.14 Sampling for a Major Industry in British Columbia

The old method of counting returning salmon involved placing a “counting fence” in a stream and counting all the fish caught by the fence. This is expensive and difficult. For example, fences are often damaged by high water.

Repeat sampling using small nets is more practical. During this year’s spawning run in the Chase River in British Columbia, Canada, you net 200 coho salmon, tag the fish, and release them. Later in the week, your nets capture 120 coho salmon in the river, of which 12 have tags.

The proportion of your second sample that have tags should estimate the proportion in the entire population of returning salmon that are tagged. So if is the unknown number of coho salmon in the Chase River this year, we should have approximately

Solve for to estimate that the total number of salmon in this year’s spawning run in the Chase River is approximately