Example:
Suppose we "banded"  1680 people (designating them as high school students).  Then we release them out into the population to mix.  Later we gathered up a sample of 500 people, of which 22 were high school students.  Could you predict the total population?

Allow students to come up with a solution.

        1680        =     22                or total population = total tagged
population total       500                                                   p hat
 

That is the basis for capture/recapture!  Once you have found a sample proportion, you can create a confidence interval about it.

Activity:
Materials:  2-3 bags of Pepperidge Farm fish, orange colored, 1 bag Pepperidge Farm fish, white colored. There are about
                          300 fish per bag.
                1 large bowl (...the pond)
                Scoop

1. Use a helper from the class to acoop out about 50 fish.  "Band" them by replacing orange fish with white fish and return them to the pond.  This is the "capture" step.

2. Mix well.

3. Recapture the fish by scooping out a sample of about 50 fish.  Count the proportion of the sample that are banded.

4. Repeat the experiment several times to see how the proportion varies.

5.  Use a different method of sampling.  Pull out fish at random until you have reached a set number of banded fish (ex. 15).  Find proportion by dividing 15 by how many had to be taken out before reaching that number.  Which method would a more accurate estimate of the population?  (the second one)

______________________________________________Worksheet______________________________________
 

Name______________________________                                                                                     Class Period______

1. Suppose that naturalists catch, tag, and release 50 deer in a forest.  After allowing time for the tagged deer to mix with the others, they catch a sample of 100 deer, 10 of which have tags.  What is the estimate for the number of deer in the forest?
 

2.  Suppose that wildlife workers capture 328 penguins on an island, mark them, and allow them to mix with the rest of the population.  Later, they capture 200 penguins, 64 of which are marked.  What is the estimate for the number of penguins on the island?
 
 

3.  Suppose that the high school in a town has 500 students.  A random survey of 200 people in the town finds 40 high school students.  What is the estimate for the number of people in the town?
 
 

4.  Visitors conducted a capture-recapture experiment to determine the number of taxicabs in Edinburgh, Scotland.  On the first day, observers saw 48 taxicabs.  The next day they observed 52 cabs, 10 of which they had seen the previous day.  What is the estimate for the number of taxicabs in Edinburgh?  What are some assumptions being made about the sample?
 
 
 

5.  In a study of raccoons in a certain region of northern Florida, 48 animals were captured using cages baited with fish heads.  The raccoons were marked and released.  In the following week, 71 raccoons were captured, 31 of which had been marked.  What is the estimate for the number of raccoons in this region?
 
 

6.  Sometimes some "trap happy" animals are easier to capture and easier to recapture than others.  Thus an animal captured the first time is also likely to be in the second sample.  What do you think this behavior will do to the estimate of the population size?
 
 

7.  In the capture-recapture method, we assume that the marks will not be removed, wear off, or become invisible in some way before the recapture.  If some animals lose their marks during the study, how will this affect the estimate of the population size?
 
 
 

8.  Suppose the time between the capture and the recapture is too long and some marked animals die.  Suppose also that some new animals are born so that the population size remains constant.  Will the deaths tend to make the estimate of the population size too large or too small?  Explain.
 

9.   To use this capture-recapture method, naturalists and statisticians must be convinced that  three basic assumptions are satisfied reasonably well.  What do you think those assumptions are, based on questions 6, 7, and 8.  (NOTE:  There are more complicated capture-recapture methods available if these assumptions cannot be satisfied.)
     1.

     2.

     3.
 
 

10.  Suppose you capture, tag, and release 100 snakes in a desert.  Then you capture a sample size of 100, 40 of which have tags.
    a.  What is the estimate for the percentage of tagged snakes in the desert?

    b.  What is the 95% confidence interval for the percentage of tagged snakes in the desert?

    c.  What is the 95% confidence interval for the number of snakes in the desert?
 
 

11.  To find out how many largemouth bass are in Dryden Lake in central New York State, a naturalist captured 213 largemouth bass and made a mark on their fins.  The fish were returned to the lake.  About a month later, the naturalist caught 104 bass, and 13 of them had marks.  Find the 95% confidence interval for the number of largemouth bass in the lake.