Question

(1 point) 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 331 people living in East Vancouver and finds that 36 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 0.05. 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,

= x / n = 36/331 = 0.108761

1 - = 1-0.10876 = 0.891239

margin of error = E = 0.05

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960

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

= (1.96/0.05)2 * 0.108761*0.891239

= 149

sample size = n = 149