The formula above for the margin of error assume that there is an infinitely large sampling theory, this assumption is reasonable when the sampling fraction is small.
2.
To adjust for a large sampling fraction, the fpc factored into the calculation of the margin of error, which has the effect of narrowing the margin of error.
3.
The margin of error for a particular sampling method is essentially the same regardless of whether the population of interest is the size of a school, city, state, or country, as long as the sampling fraction is less than 5 %.
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