Final answer:
The size of the confidence interval increases as the level of confidence increases because a higher confidence level requires capturing a larger area under the distribution curve, leading to a wider band to maintain increased certainty.
Step-by-step explanation:
When asking what happens to the size of the confidence interval as the level of confidence increases, there is a direct relationship to consider. As the level of confidence increases, the confidence interval band becomes wider. This occurs because a higher level of confidence means that we wish to be more certain that our interval contains the true parameter value. Therefore, more of the distribution must be included within the interval to maintain this higher certainty.
For instance, a 99 percent confidence interval will be wider than a 95 percent confidence interval because it includes a larger portion of the distribution, aiming to capture the true parameter with 99 percent certainty as opposed to 95 percent. This is because increasing the confidence level increases the error bound, which is the amount of uncertainty associated with the estimate of the true population parameter, hence resulting in a broader interval. Conversely, decreasing the confidence level would decrease the error bound and produce a narrower interval.