SOLUTION: After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to jus

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Question 1181457: After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be: *
2 points
4000.
1600.
800.
200.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The standard error for population sample proportion is s%5Be%5D+=+sqrt%28%28p%281-p%29%29%2Fn%29.
It is initially known that sqrt%28%28p%281-p%29%29%2F400%29+=+0.05.
==> %28p%281-p%29%29%2F400+=+0.05%5E2+=+1%2F400 ===> p%281-p%29+=+1.
Then from the new requirement of a standard error of 0.025,
sqrt%28%28p%281-p%29%29%2Fn%29+=+sqrt%281%2Fn%29+=+0.025, we get 1%2Fn+=+0.025%5E2+=+1%2F1600, after squaring both sides.

From this we get highlight%28n+=+1600%29.