Final answer:
The width of a confidence interval indicates precision, with a narrower interval signifying higher precision. As the level of confidence increases, the interval becomes wider, reflecting lower precision but higher certainty.
Step-by-step explanation:
The width of the confidence interval is inversely related to the precision of an estimate. A narrower interval indicates higher precision because it suggests that the estimate is more concentrated around the true parameter value. On the other hand, a wider interval indicates lower precision as it covers a broader range of values, reflecting greater uncertainty about the parameter's true value. This can be illustrated by comparing confidence intervals with different confidence levels. For example, a 95 percent confidence interval will be wider than a 90 percent confidence interval because it is designed to capture the true population parameter with greater certainty, thus it includes a larger range of values. Conversely, increasing the level of confidence from, say, 95 percent to 99 percent will result in a wider interval to encompass more of the distribution's range, therefore offering a higher level of certainty at the expense of precision.
In summary, the correct answer to the student's question is that a narrower interval indicates higher precision (option b).