Question

Refer to the following scenario. 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 330 people living in East Vancouver and finds that 31 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 =

IT IS NOT 125.85 or 126.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.05

The provided estimate of proportion p is, p = 0.0939
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.0939*(1 - 0.0939)*(1.96/0.05)^2
n = 130.74

Therefore, the sample size needed to satisfy the condition n >= 130.74 and it must be an integer number, we conclude that the minimum required sample size is n = 131
Ans : Sample size, n = 131

if you take z value upto 2 or 4 decimal answer would be change