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Sample size and finite population correction factor

The house of representatives has a very controversial bill that will be going to vote. To help formulate his strategy on how to get the bill passed, the chairman of the committee that has been studying the bill wishes to know if there is a division between Democrats and Republicans on the issue or if there is some other basis for the split. To estimate the proportion of Republicans in favor of the bill, how large must a sample of representatives be to estimate the percentage within 3 percentage points with 90% certainty. Assume there are 538 representatives. Use the finite population correction factor and develop your own formula for computing the answer.

Please show all formulas.
Answer should be n<= 314.

Solution Preview

See the attached file.
sp=standard error of proportion=square root of (pq/n) square root of ((N-n)/(N-1))
where square root of ((N-n)/(N-1)) is the finite population multiplier
where N is the population size and n is the sample size

confidence interval= 90%
We have to find z corresponding to 5% in ...

Solution Summary

The sample size for estimating proportion has been calculated and the details are provided.