What effect does increasing the confidence level have on a confidence interval?
I know that increasing the confidence level increases the error bound, making the confidence interval wider. Decreasing the confidence level decreases the error bound, making the confidence interval narrower, but why?
To answer this question we look at the formula of the confidence interval, say for the confidence interval for the mean:
We conclude from above that the width of the confidence interval is directly proportional to Zc.
Now we look at the z table for different level of significance
As you can see z value increases with the increase in the confidence level. At 95% two-tailed confidence level it is 1.96 which increases to 2.576 at a two-tailed 99% confidence level. From the above relation we now the width of the confidence interval is directly proportional to Zc. Hence we can conclude as the confidence interval increases, the confidence interval becomes wider and vice versa.
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