Let $ X = (X_1, ..., X_n)$ be a vector observation collected from Normal Distribution. We don't know neither variance of population nor expected value. We would like to estimate expected value for population. So we should use T-distritbution, I mean: $t = \frac{\overline{X} - \Theta }{ \sigma(\overline X)}$

To compute $\sigma(\overline X)$ we need a standard deviation of popluation but we haven't got it. So it is proposed to get standard deviation of sample instead of it.

I don't understand why standard deviation of sample will be certainly good choice.


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