The breadth of the confidence interval grows as the confidence level does. The breadth of the confidence interval reduces as the confidence level rises.
Generally speaking, the more information we know on the level of the population parameter, the narrower a confidence interval becomes. As a result, we want to make sure that all of the confidence intervals are as small as feasible. So let's look at the variables that influence the mean's t-interval width.
The margin of error grows as the degree of confidence does because we require a broader interval to improve our level of confidence that the interval includes the population mean.
Because the standard error is reduced as sample size increases, confidence intervals are narrower.
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