Final answer:
A confidence interval based on a sample size of n = 100 will be wider than one based on a sample size of n = 400 because the margin of error decreases with a larger sample size, leading to a narrower interval.
Step-by-step explanation:
When the level of confidence and sample proportion p' remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400. The margin of error for a confidence interval decreases as the sample size n increases, given by the formula for the standard error of the sample proportion which is √(p'(1-p')/n). Therefore, with a larger sample size, the estimate becomes more precise, and the confidence interval becomes narrower. Conversely, with a smaller sample size, the estimate is less precise, and the confidence interval is wider.