Question

The overall U.S. prevalence rate of flu during the month of February 2016 was 9%. During the same time period, the Louisiana Dept of Health conducted a survey to estimate flu prevalence in Louisiana. Of the 400 survey respondents, 50 reported having the flu during the month of February 2016 resulting in an observed prevalence rate (or proportion of individuals with the flu) of 12.5%. Based on the results of the survey, construct a 95% CI for p, the population prevalence (proportion of population) of flu in LA during February 2016.

Answer 1

Sample proportion = 50 / 400 = 0.125

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 -) / n ] < p < + Z/2 * sqrt [ ( 1 -) / n ]

0.125 - 1.96 * sqrt( 0.125 * ( 1 - 0.125) / 400) < p < 0.125 +1.96 * sqrt( 0.125 * ( 1 - 0.125) / 400)

0.093 < p < 0.157

95% CI is ( 0.093 , 0.157 ) ​​​​​​​