Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.
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Why confidence interval is useful
The confidence interval becomes smaller.
no,these are not the same thing.The values at each end of the interval are called the confidence limits.
The width of the confidence interval increases.
Narrow because there is less of a chance for people to mess up