A researcher tags 20 squirrels in a wood. The next month, she returns to the wood and observes a sample of 12 squirrels, 5 of which are tagged, and a sample of 25 squirrels, 9 of which are tagged. If the two samples are representative of the squirrel population, which is the best estimate of the number of squirrels in the wood?
To estimate the number of squirrels in the wood based on the tagging method, we can use the concept of proportion.
For the first sample of 12 squirrels, 5 of them are tagged. This means that 5/12 = 0.4167, or 41.67% of the sample is tagged.
For the second sample of 25 squirrels, 9 of them are tagged. This means that 9/25 = 0.36, or 36% of the sample is tagged.
We can then use these percentages to estimate the total number of squirrels in the wood.
If we assume that the proportion of tagged squirrels in the samples is representative of the proportion of tagged squirrels in the entire population, we can set up a proportion:
0.4167 (proportion of tagged squirrels in first sample) = x (total number of squirrels) / 12 (total number of squirrels in first sample)
Solving for x, we get:
x = 0.4167 * 12
x = 5
Similarly, for the second sample, we have:
0.36 = x / 25
x = 0.36 * 25
x = 9
Taking the average of these two estimates:
(x1 + x2) / 2 = (5 + 9) / 2
x = 14
Therefore, the best estimate of the number of squirrels in the wood based on the tagging method is 14 squirrels.