Two studies were completed in Georgia. One study in northern Georgia involved 3,000 patients 84% of them experienced flulike symptoms during the month of December. The other study in southern Georgia, involved 2,000 patients 75% of them experienced flulike symptoms during the same month. Which study has the smallest margin of error for a 99% confidence interval?

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Two studies were completed in Georgia. One study in northern Georgia involved 3,000 patients 84% of them experienced flulike symptoms during the month of December. The other study in southern Georgia, involved 2,000 patients 75% of them experienced flulike symptoms during the same month. Which study has the smallest margin of error for a 99% confidence interval?

Mathematics
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northern with a margin error of 1.7
The margin of error for a 99% confidence interval for each study can be found as follows: \[\large MoE(N.Ga)=2.576\sqrt{\frac{0.84(1-0.84)}{3000}}\] \[\large MoE(S.Ga)=2.576\sqrt{\frac{0.75(1-0.75)}{2000}}\] Note: The margin of error can be converted into a percentage, if necessary, by multiplying by 100.

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