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Unformatted text preview: rror of the mean. If population size, N , is ﬁnite and not too large compared n, a correction is required:
¯ N −n √
N −1 n (You are not responsible of this last sentence in the exam.) Utku Suleymanoglu (UMich) Sampling Distributions 11 / 21 Sampling Distributions σ
σx = √
Think about the relationship between variance of x and sample size!
We are trying to estimate µ with X .
We know our estimator is unbiased, so it is aiming at the correct target.
What does the σx measure?
How dispersed the X numbers around µ!
Do you want a small SE or a big one?
SE of the mean determines the precision of the X .
Depends on two things:
σ 2 : The variance of the observations in the sample. We usually don’t observe this
either. Even if we do observe this, we can’t change this to make our estimates more
n: Sample size. More observations, more info, more precision. Utku Suleymanoglu (UMich) Sampling Distributions 12 / 21 Sampling Distributions Distribution of Random Variable that is X
We now know that X...
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- Spring '08