Final answer:
To determine the minimum sample size for a survey with a margin of error of 0.03 and a 99% confidence level, use the error bound formula with Z-score for 99% confidence and assume 0.5 for the population proportion if no preliminary estimate is available.
Step-by-step explanation:
When attempting to determine the minimum sample size needed for a survey to have a specific margin of error at a given confidence level, the error bound formula is used. For a margin of error (ME) of 0.03 and a 99% confidence level, we need to first identify the Z-score associated with a 99% confidence level, which is typically 2.576. Then, assuming we do not have a preliminary estimate of the population proportion (p), we use 0.5 for the calculation as this maximizes the required sample size.
The formula to calculate sample size (n) is n = (Z^2 * p * (1-p)) / ME^2. Plugging our values in, we would calculate n = (2.576^2 * 0.5 * (1-0.5)) / 0.03^2, which will yield the required sample size to achieve the specified margin of error and confidence level. If the margin of error or the confidence level changes, the sample size required would also change accordingly.