To understand the problem. let us consider a situation,
Suppose we want to construct confidence interval for population mean µ of normal population as,
Width of confidence interval =
You can see that that the width of a confidence interval is directly proportion to i.e the standard deviation. Thus, if we have two different populations with the same mean but different standard deviations and it is need to make two confidence intervals, one from each sample, and these intervals have the same confidence level, Condidence interval will be larger for such sample whose standard deviation is larger and Condidence interval will be smaler for such sample whose standard deviation is smaller.
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