SOLUTION: A random sample of 500 fish is taken from a lake, marked, and returned to the lake.after a suitable interval a second sample of 500 is taken and 25 of these are found to be marked.

Question 533198: A random sample of 500 fish is taken from a lake, marked, and returned to the lake.after a suitable interval a second sample of 500 is taken and 25 of these are found to be marked. by considering the number of fish marked in the second sample,
1)Estimate the number of fish in the lake
2)By considering the confidence interval for the proportion of marked fish in the lake, obtain a 95% confidence limits for the number of fish in the lake
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A random sample of 500 fish is taken from a lake, marked, and returned to the lake.after a suitable interval a second sample of 500 is taken and 25 of these are found to be marked. by considering the number of fish marked in the second sample,
1)Estimate the number of fish in the lake
Let the population be "x":
x/500 = 500/25
x = 20*500
x = 10,000
-------------------------
2)By considering the confidence interval for the proportion of marked fish in the lake, obtain a 95% confidence limits for the number of fish in the lake
---
p-hat = 500/10,000 = 0.05
---
ME: = 1.96*sqrt[0.05*0.95/500] = 0.0191
-----
95% CI: 0.03 <= p <= 0.07
===================================
So, if proportion of marked fish is 0.03, # of fish = 500/0.03 = 16,667
And, if proportion of marked fish is 0.07, # of fish = 500/0.07 = 7143
----
95% fish population : 7143<= x <= 16,667
=================
Cheers,
Stan H.
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