Using Cochran’s formula, at 95% confidence and 50% prevalence, to calculate sample size
Cochran's formula for calculating sample size is:
n = Z^2 * p * (1-p) / E^2
Where:
n = required sample size
Z = Z score for the desired confidence level (Z = 1.96 for 95% confidence)
p = estimated prevalence or proportion in the population (50% in this case)
E = margin of error (typically set at 5%)
Plugging in the values:
n = (1.96)^2 * 0.5 * (1-0.5) / (0.05)^2
n = 3.8416 * 0.25 / 0.0025
n = 0.9604 / 0.0025
n = 384.16
Therefore, the required sample size is 385 at 95% confidence level and a 50% prevalence rate.