Question: Assume that two populations have the same variance 2. If a sample of size n1 produced a variance S12 from population I and a sample

Assume that two populations have the same variance Ïƒ2. If a sample of size n1 produced a variance S12 from population I and a sample of size n2 produced a variance S22 from population II, show that the pooled variance

is an unbiased estimator of Ïƒ2. Show that (S12 + S22) / 2 is also an unbiased estimator of Ïƒ2. Which of the two estimators would you prefer? Give reasons for your choice.

(m 1)S; + (n2 - 1)S ni +m -2

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