How Accurate is the Fish Population Estimate in the Lake?

[Alexsandro]

Researchers of a department of engineering of fish are studying the fish of a lake. In the first phase of the work they collect 100 fish, place labels in all they and they return them to the lake. One week later them they come back to the lake, they collect more 100 fish and they observe that 7 of them possesses labels.

(a) Which the best estimate for the number of fish in the lake?

(b) That assumptions must be satisfied to justify the estimate of the previous item ?

 

[mathman]

(a) N=100(100/7)=1428

(b) Extrapolation - since 7/100 of the caught fish were tagged, assume that 7/100 times (N) total number of fish = total number of that have been tagged (=100).

 

[tacman]

(a) The best estimate for the number of fish in the lake would be 1,428 fish. This can be calculated by taking the total number of fish collected (200) and dividing it by the proportion of fish with labels (7/100). This gives us a ratio of 1 fish with a label for every 28.57 fish in the lake. Multiplying this ratio by the total number of fish collected (200) gives us an estimate of 1,428 fish in the lake.

(b) In order to justify this estimate, the researchers must assume that the fish population in the lake is representative of the entire lake and that the fish are evenly distributed throughout the lake. They must also assume that the fish with labels are a random sample of the entire fish population and that there is no bias in the labeling process. Additionally, the researchers must assume that the fish do not migrate in and out of the lake during the week between collections, which could affect the accuracy of the estimate. Finally, the researchers must also assume that there are no significant changes in the fish population during the week between collections, such as breeding or mortality.