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Suppose that we have 2 independent samples $X_{11}, X_{12},.., X_{1n_1}$ and $X_{21}, X_{22},.., X_{2n_2}$ from a normally distributed population with $n_1<n_2$. Does that mean that the sample variance of the first sample is more efficient in the estimation of the population variance, versus the sample variance of the second sample?

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    $\begingroup$ If you were to use only the first $n_1$ elements of the second sample, how efficient would that be compared to using the first sample? Now draw your conclusions. $\endgroup$
    – whuber
    Dec 7, 2018 at 21:07
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    $\begingroup$ Well, I suppose that the sample variance of the second sample is more efficient. $\endgroup$
    – George
    Dec 8, 2018 at 18:01

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