Final answer:
The minimum sample size can be calculated using the formula n = (Zα/2^2 * p' * q') / E^2, substituting 0.5 for both p' and q' and the Z-value for a 99% confidence level, which is approximately 2.576. Solve for n and round up the result.
Step-by-step explanation:
The student is asking about the minimum sample size required to estimate a population proportion, given a margin of error, a confidence level, and unknown population proportion values p and q. The standard formula to calculate the required sample size for a proportion is n = (Zα/2^2 * p' * q') / E^2, where Zα/2 is the critical value for the confidence level, p' is the estimated proportion of successes, q' is 1 - p', and E is the margin of error.
Since p and q are unknown, it is common to use 0.5 for both to maximize the product p'q', as this gives the largest sample size estimate. For a 99% confidence level, the Z-value (Zα/2) is approximately 2.576. Plugging these values into the formula gives:
n = (2.576^2 * 0.5 * 0.5) / 0.018^2
Solving for n, we find the minimum sample size needed. Always remember to round up the final value of n to ensure the sample size is sufficient.