Question

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 336 people living in East Vancouver and finds that 37 have recently had the flu.

Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps.

Sample size =

Answer 1

Solution :

Given that,

n = 336

x = 37

Point estimate = sample proportion = = x / n = 37 / 336 = 0.11

1 - = 1 - 0.11 = 0.89

margin of error = E = 0.04

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.04 )2 * 0.11 *0.89

= 235.05

sample size = n = 236