| Since many high school teachers don't have access to Minitab or other statistics software packages,
I thought I would add that a simple capture/recapture experiment can be simulated on the TI-82 if
the population is limited to less than 100 to fit the lists. I will assume a population of p=85, a capture
of c=20, a recapture of r=15: 1) Enter as many 0's as there is in the population in list 1. 2) Tag as many as the first capture by turning the 0s to 1s. For a population of 85 and 20 captured and tagged, L1 should now have 65 zeros and 20 ones. 3) Use the sequence command to fill L2 with a list of random numbers until it's dimension matches the population. 4) Sort L2 and L1 by L2. 5) The first r numbers in L1 now represent the recaptured items, and the sum will be the number of tagged items recaptured. These steps are easy to write into a short program so that the students need only to push the enter key to rerun the experiment, but the method of sampling without replacement demonstrated is worth working through with the students so they will be able to simulate such situations on their own. I don't know if very many people have the simulation software from Resampling Stats, but it will quickly run several hundred simulations of the capture/recapture for larger populations, produce the mean, median, distribution of results, and breakout the 90th percentile (or other percentages of choice) limits to show both the right skew of the distribution and the variability that Bruce spoke of. Regarding the use of this method for the census... My mathematical instinct leads me to believe that both a large number of tagged items in the recapture and a large percentage of tagged items in the recapture (they are different) will minimize the error. I would think that for values as large as the census would use, the error would not be very large, at least in percentage terms. And as always, |