Two studies were completed in Florida. One study in northern Florida involved 2,000 patients; 64% of them experienced flulike symptoms during the month of December. The other study, in southern Florida, involved 3,000 patients; 54% of them experienced flulike symptoms during the same month. Which study has the smallest margin of error for a 95% confidence interval?

Given:Northern Florida: 2,000 patients ;  64% experienced flulike symptoms during DecemberSouthern Florida: 3,000 patients ; 54% experienced flulike symptoms during December
Standard error = √[p(1-p)/n]
NF = √[0.64(1-0.64)/2000] = √[(0.64*0.36)/2000] = 0.0107 or 1.07%SF = √[0.54(1-0.54)/3000] = √[(0.54*0.46)/3000] = 0.0091 or 0.91%
smallest margin of error for a 95% confidence interval
NF: Em ≈ 0.98/√2,000 = 0.98/44.72 = 0.0219 or 2.19%SF: Em ≈ 0.98/√3,000 = 0.98/54.77 = 0.0178 or 1.78%
MY ANSWER:
The southern Florida study with a margin of error of 1.8%.