California's salmon season has been officially caled off for the second straight year. Fishery managers canceled all commercial and sport fishing as scientists struggle to figure out why the Cinook salmon population has collapsed.

The decision to shut down the season was a relatively easy one, says Frank Lockhart, head of sustainable fisheries for the Pacific Fisheries Management Council. The Chinook salmon population has declined dramatically over the past two years .

 

The Question: How do they know the current Chinook salmon population? One Method: Tag, Release, then sample. 1. Start by tagging a known number of salmon. Call this number y. 2. Let N denote the salmon population in the given region (unknown). 3. Then the population proportion of tagged fish is p= y/N. 4. Later, sample the population of salmon. You let the fisherman do this. They are required, by law, to report how many salmon they have caught, and how many of these were tagged. 5. Let n (sample size) be the total number of salmon caught, and r (successes) denote the number of these that are tagged. The proportion of tagged fish in the sample is then p = x/n. 6. It stands to reason that p p = #. 7. Now, you know p and y, then you rearrange the equation to be N y/p. There you have a point estimate for the number of salmon. 8. To improve matters, you caleulate a 95% confidence interval for p. Use the upper limit and lower limit to get a 95% confidence interval for the number of salmon. Give it a try: Suppose the Pacific Fisheries Management Council tags 5,000 salmon before the start of the season. During the season, fisherman report that of 1,562,500 salmon caught, 1,250 were tagged. Find the point estimate for N (the population size) and the 95% confidence interval for N.