A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 8% margin of error at a 99% confidence level, what size of sample is needed?
To determine the sample size needed for the poll, we can use the formula:
n = (Z^2 * p * q) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level corresponds to a Z-score of 2.57)
p = estimated proportion of support for the candidate (we'll assume 50% in this case to ensure the largest sample size)
q = 1 - p (rest of the population, which is 1 - 0.5 = 0.5)
E = desired margin of error (8% or 0.08)
Plugging in the values:
n = (2.57^2 * 0.5 * 0.5) / 0.08^2
n = (6.6049 * 0.25) / 0.0064
n = 1.651225 / 0.0064
n ≈ 258.295
Therefore, a sample size of at least 259 individuals is needed for the poll.