Question

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?

Answer 1

The MoE for a 99% confidence interval in Northern Georgia is:
$2.576 \sqrt{\frac{0.84(1-0.84)}{3000}}=0.017$
The MoE for a 99% confidence interval in Southern Georgia is:
$2.576 \sqrt{\frac{0.75(1-0.75)}{2000}} =0.025$
Therefore the Northern Georgia study has the least margin of error.