utku suleymanoglu umich sampling distributions 11 21

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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: σx = ¯ N −n √ σ . 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 = √ ¯ n 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 precise. 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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