X 1 and S 2 1 are the sample mean and sample variance from a population with
Question:
X̅1 and S21 are the sample mean and sample variance
from a population with mean μ1 and variance σ12. Similarly,
X̅2 and S22 are the sample mean and sample variance from a
second independent population with mean μ2 and variance σ22.
The sample sizes are n1 and n2, respectively.
(a) Show that X1 − X2 is an unbiased estimator of μ1 − μ2.
(b) Find the standard error of X̅1 − X̅2. How could you estimate
the standard error?
(c) Suppose that both populations have the same variance; that
is, σ21 = σ22 = σ2. Show that
is an unbiased estimator of σ2.
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Related Book For
Applied Statistics And Probability For Engineers
ISBN: 9781118539712
6th Edition
Authors: Douglas C. Montgomery, George C. Runger
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