Final answer:
The width of a confidence interval is smaller with a larger sample size, as increased sample sizes provide more precise estimates of the population parameter, and conversely, the width is larger with a smaller sample size due to increased variability.
Step-by-step explanation:
The width of a confidence interval (CI) for a population mean is smaller if the sample size is larger. When the sample size increases, the error bound decreases, making the confidence interval narrower. Conversely, a smaller sample size results in more variability, requiring a larger interval to capture the true population mean. This is because a smaller sample does not estimate the population parameters as precisely as a larger sample, thus a wider interval is needed to ensure the same level of confidence. Additionally, changing the confidence level also affects the width of the CI; for example, a 99 percent confidence interval is wider than a 95 percent confidence interval because it accounts for a larger portion of the distribution, aiming to include more of the population data. Therefore, the correct answer is (B) The width of a confidence interval is larger with a smaller sample size.