How to get the population standard deviation from a sample standard deviatoinI am trying to find the confidence interval, and I need to know the population standard deviation. If I am given the sample standard deviation, how can I get the population one? Thanks!

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lildeutsch11xq2j · Accepted Answer

You need to use s2 unbiased estimator for σ2 population variance which is defined asσ2=1N∑i=1N(xi−μ)2The σ2 computation would require to know μ true mean which is unknown when working with a sample so again you need an estimator for this which is x― sample mean.The use of x― sample mean instead of μ true meam introduces a bias which tends to zero as the sample numerosity grows so the sample variance estimator uses a corrective terms2=1N−1∑i=1N(xi−x―)2As you can see, with N→∞ you get s2→σ2 as - x―→μ- N−1→N

titemomo8gjz · Accepted Answer

Generally speaking, if you are taking a sample from a normal distribution and you are trying to obtain a confidence interval for the mean, but you don&#039;t know the population standard deviation, the two-sided confidence interval at level of significance 1−α isX―±tα2Snwhere tα2 is the positive number such that P(T&amp;gt;tα2)=α2 when T is a Student&#039;s t-distributed random variable with n−1 degrees of freedom. Here tα2 is a little bit larger than zα2 (which arises from the standard normal distribution), which is what you would use if the population standard deviation were known.

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