Question

There have been about 566 cases of H5N1 human infection (the “bird flu”) reported worldwide in the last decade. In 332 of these cases the patients have died, a proportion of 58.66%. A 95% CI for the “true” overall proportion of deaths is: a. (56.7%, 60.7%) b. (54.6%, 62.7%) c. (58.6%, 58.8%) d. (9%, 97%)

What is the standard error of the sample proportion given in the last problem? a. 0.0207 b. 0.0406 c. 0.5866 d. 0.0341 e. Cannot be determined. / Too little information.

Answer 1

Sample proportion = 332 / 566 = 0.587

95% confidence interval is
p̂ ± Z(α/2) √( (p * q) / n)
0.587 ± Z(0.05/2) √( (0.5866 * 0.4134) / 566)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.587 - Z(0.05) √( (0.5866 * 0.4134) / 566) = 0.546
upper Limit = 0.587 + Z(0.05) √( (0.5866 * 0.4134) / 566) = 0.627

95% Confidence interval is ( 54.6 % , 62.7 % )