We shouldn’t have to give up confidence in order to have a smaller (more precise) interval estimate. In this video I cover all of the other factors that we can change to affect the width of the confidence interval, and I discuss why increasing the sample size is by far the best approach.
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Doubling the population standard deviation s has the effect of doubling the width of the confidence interval estimate of m.
When constructing confidence interval estimate of μ, doubling the sample size n decreases the width of the interval by half.