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An estimation question
Posted:
Apr 28, 2012 11:18 AM
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This problem occurs a lot in real life..
You sample n people, and a proportion p of them are found to be
carrying a red flag (like some political party, prefer a brand of soap
etc.). Textbooks say that the estimate of the proportion carrying the
red flag in the total population is p with a variance of n.p.(1-p).
This would indicate that p close to 0 or 100 pct can be estimated with
smaller samples than p around 50 pct with the same confidence.
But suppose we have carried out these samplings repeatedly and past
results show that the proportion carrying the red flag always comes in
between 0 and say 15 pct. We can even estimate a histogram
distribution of p from past samples. If we now make a new sampling of
n items - and we wish to rely on the past sampling results, how would
the mean and variance estimates change?
Thanks for any replies.
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