Posted by christine on Friday, September 8, 2006 at 4:53pm.
Estimate a population:
To study a species of fox, a team captures and tags 25 foxes from a large forest and then releases them. The following week they capture 15 foxes and find 5 are tagged. Estimate the number of foxes in the forest.
This is a proportion problem.
We know that 25 are tagged.
Let P denote the population, then
That is, the ratio of the tagged to the population should be approximately the ratio of the caught tagged to the caught untagged. Thus
The main hypotheses used is that the tagged have had sufficient time to be randomly dispersed throughout the population and that the sample is collected randomly from the population.
what roger said he seems to be a smart person!
Ahhh!! I see! It is a small population of foxes (being that after a full week, 5 of the original 25 were caught (in a small group of 15).
So, in the beginning, the 25 foxes (sample) of the whole forest, and the next sample, was 5 of the 15. The # of foxes chosen from whole pop. (that's where you got ratio 1 from.
Yes! That's the idea here. We're using a sample to make some estimate of the population. However, in my post I see I stated it incorrectly. I should've stated that the ratio is caught tagged to total caught, not just total caught untagged.
The answer you should get is 75 as an estimate for the population. I should comment that there is a probability distribution called the hypergeometric distribution based on this sampling technique, but that will have to wait for a more advanced course.
i think its 40 that's a tricky!
Now quit guessing and reason it out.
If A=1+r^a+r^2a+r^3a+.......................to infinity
then find a/b=?????
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