Can someone help me do this problem?
A group of environmentalist are trying to estimate the population of the state rid in clear view park. They capture a sample of 500 birds in early spring and tag them. in august they capture 215 birds, of which 20 are tagged.
a) use the capture recapture method to find a central estimate of the population
b) estimate the population with a 95 percent confidence level
c)what objections can you raise to the way the capture recapture method was applied to estimate the population?
a) Use ratio and proportion...
500 tagged birds/n total birds = 20/215
by cross products:
20n = 500 * 215
20n = 107,500
n = 107,500 / 20 = 5,375
b) ?
c) In early spring the recently hatched baby birds are probably not available for capture, as they are still in the nest. However, by August they would be available for the recapture. Therefore, the first capture data is not very sound, as the total population was underrepresented in the capture process.
Sure, I'd be happy to help you with this problem!
a) To find the central estimate of the population using the capture-recapture method, we can use the formula:
Population estimate = (Number of individuals in the first sample * Number of individuals in the second sample) / Number of individuals in both samples.
In this case,
Number of individuals in the first sample = 500
Number of individuals in the second sample = 215
Number of tagged individuals in the second sample = 20
So the central estimate of the population would be:
Population estimate = (500 * 215) / 20
You can calculate this to get the actual estimate of the population.
b) To estimate the population with a 95 percent confidence level, we can use the Lincoln-Petersen index and calculate the upper and lower limits of the confidence interval.
The formula to calculate the confidence interval is:
Lower limit = Population estimate - (1.96 * Standard error)
Upper limit = Population estimate + (1.96 * Standard error)
To calculate the standard error, we can use the formula:
Standard error = (Number of individuals in the first sample * Number of individuals in the second sample) / (Number of tagged individuals in the second sample * Number of individuals in both samples)^0.5
Using the values from the problem, you can calculate the standard error, then substitute it into the confidence interval formula to find the estimate with a 95 percent confidence level.
c) Now, let's discuss the objections raised to the way the capture-recapture method was applied to estimate the population.
1. Assumption of equal probabilities: The capture-recapture method assumes that each individual in the population has an equal chance of being captured. This assumption may not hold true in practice, as certain birds may have higher or lower probabilities of being captured due to various factors like behavior, habitat, or accessibility.
2. Time frame: The capture-recapture method assumes that the population remains constant between the two capture events. However, in reality, populations can change due to migrations, births, deaths, or other ecological factors. If there are significant changes in the population during the time period, the estimate may not be accurate.
3. Tag loss or tag-induced mortality: There is always a possibility that some tagged individuals may lose their tags or die, thus affecting the accuracy of the population estimate. The capture-recapture method assumes no loss of tags and that all tagged individuals have an equal chance of being recaptured. These assumptions may not hold true, leading to biased estimates.
4. Sample size and representativeness: The accuracy of the population estimate can be influenced by the size and representativeness of the samples taken. If the sample size is not adequate or the samples are not representative of the entire population, the estimate may be biased.
It is important to consider these objections and limitations when interpreting the results obtained from the capture-recapture method.