What happens if the confidence level of an interval is increased?

When the confidence level of an interval is increased, the interval becomes wider. This is because a higher confidence level indicates that we want to be more certain that the interval contains the true parameter we are estimating. To achieve this increased certainty, the range of values that we include in the interval must increase, resulting in a wider interval.

For example, if we were to calculate a 95% confidence interval, we would include a certain range of values based on our sample data and the variability within that data. If we then increase the confidence level to 99%, we would need to account for more variability and uncertainty in our estimates, leading to a larger range of values to ensure that the true parameter falls within this broader interval.

This concept reflects the trade-off between confidence and precision: as we aim to capture a higher level of confidence, we sacrifice some precision by making the interval wider.