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Context of this question is not clear because it is NOT a full question. However

when attempting to estimate an parameter such as µ using sample data when

the population standard deviation σ is unknown, we have to estimate the standard

deviation of the population using a stastitic called s where

_

Σ(x-x)²

s = ▬▬▬▬

n -1

_

and estimator for µ , in particular x

........................................._

has a standard deviation of s(x)= s/√n

and the statistic

_

x - hypothesized µ

T = ▬▬▬▬▬▬▬▬▬▬

s

has a student's T distribution with n-1 degrees of freedom

If n> 30 , then by the Central Limit Theorem, the T distribution

approaches the shape and form of the normal(gaussian) probability

distribution and the Z table may be used to find needed critical statistical

values for hypothesis tests , p-values, and interval estimates.

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Q: When the population standard deviation is not known?
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