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Does a low standard deviation equate to a low (narrow) confidence interval?

Does a low standard deviation equate to a low (narrow) confidence interval?

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Answer #1

Confidence interval is given by, CI = Mean Z* ,

where is the standard deviation, n is the sample size and Z* is the critical value.

If all other values are kept constant, a ;lower standard deviation means, will be smaller value and hence, the width of the confidence interval will also decrease.

So, a low standard deviation equate to a low (narrow) confidence interval, provided that all other values remain constant.

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