The confidence interval becomes wider when the confidence level increases because a higher confidence level requires a broader range of values to ensure that the true population parameter is captured within that interval. Essentially, increasing the confidence level means we want to be more certain that our interval includes the true value, which necessitates a larger margin of error. This trade-off between confidence and precision results in a wider interval. Thus, while we gain more confidence in the estimate, the precision of our estimate decreases.
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