Solve each problem. Capture-recapture method. To estimate...

Solve each problem. Capture-recapture method. To estimate the size of the grizzly bear population in a national park, rangers tagged and released 12 bears. Later it was observed that in 23 sightings of grizzly bears, only two had been tagged. Assuming the proportion of tagged bears in the later sightings is the same as the proportion of tagged bears in the population, estimate the number of bears in the population.

Solve each problem.
Capture-recapture method. To estimate the size of the grizzly bear population in a national park, rangers tagged and released 12 bears. Later it was observed that in 23 sightings of grizzly bears, only two had been tagged. Assuming the proportion of tagged bears in the later sightings is the same as the proportion of tagged bears in the population, estimate the number of bears in the population.

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Key Concepts

Capture-Recapture Method

This method is used to estimate the size of a population by capturing a sample of individuals, marking or tagging them, releasing them, and then later recapturing or observing a new sample. The method relies on the key assumption that the marked individuals have thoroughly mixed with the entire population between the tagging and recapture phases, thereby making the second sample representative of the whole population.

Proportional Reasoning in Sampling

This concept involves assuming that the ratio of tagged individuals in the second sample is equivalent to the ratio of tagged individuals in the overall population. By setting up this proportional relationship, one can solve for the total population size. Proportional reasoning is fundamental in many estimation techniques when direct counting is impractical.

Population Estimation Using Ratios

This concept refers to using the established ratio between tagged individuals and the total population to derive an estimate. The typical formula, known as the Lincoln-Petersen estimator, equates the proportion of tagged individuals in the recaptured sample to the proportion initially tagged in the full population, allowing for an algebraic solution to estimate the population size.

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