| |
Capture-Tag-Recapture
Bud Terfli owns 10 acres of property. He's amazed at
all the butterflies he sees. He wonders...
How many are there? I'd like to know, but I can't
possibly count them all.
Bud consults a statistician, who tells him about a
method that produces an estimate of the population size.
The method is called Capture-Tag-Recapture.
- Capture
- Bud captures 150 butterflies. He's selected them
using a method called random sampling. That is,
each possible collection of 150 butterflies was
equally likely to have been the captured
collection of 150 butterflies.
- Tag
- Bud tags--or marks--each of the 150 butterflies.
Each now has a harmless white spot on its left
wing. Bud releases the butterflies.
- Recapture
- A few days later (the previously captured
butterflies have had ample time to distribute
themselves about the property) Bud again collects
butterflies--this time he collects a random
sample of 200 butterflies. Some of them have
white spots, some don't. In fact, exactly 17 of
them have a white spot on the left wing.
The statistician provides an on-the-spot estimate of
the total number of butterflies on Bud's property. Can
you?
- What number does the statistician report to Bud?
Describe the reasoning you use to arrive at this
value.
- Is this number correct? That is, is this number
exactly equal to the true number of butterflies
on Bud's property?
- What practical difficulties arise when using this
method?
|
|