Question

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?
A.The northern Florida study with a margin of error of 1.8%.
B.The southern Florida study with a margin of error of 1.8%.
C.The northern Florida study with a margin of error of 2.1%.
D.The southern Florida study with a margin of error of 2.1%.

Answer 1

Given:
Northern Florida: 2,000 patients ;  64% experienced flulike symptoms during December
Southern 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:

B.The southern Florida study with a margin of error of 1.8%.

Answer 2

Because a larger sample size is always more accurate (if unbiased) the southern Florida one is right. I took the test, B is correct.