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Utku Suleymanoglu (UMich) Sampling Distributions 18 / 21 Sampling Distribution of P Example If you know that 20% of all university students come from families with no university
education, what is the probability that a randomly chosen sample of 100 students have
sample proportion between 16% and 24%?
There is another way of solving this question. See homework.
We know that we can approximate the distribution of P with
N (p , p (1 − p )/100) = N (0.2, 0.0016) as long as np (1 − p ) > 5.
Then calculate the P (0.16 < P < 0.24) approximately by:
0.16 − 0.2
0.24 − 0.2
= P (−1 < Z < 1) = F (1) − F (−1) P (0.16 < P < 0.24) ≈ P ( = 0.8413 − 0.1587 = 0.682 Utku Suleymanoglu (UMich) Sampling Distributions 19 / 21 Properties of Estimators Unbiased Estimators As mentioned before an estimator is unbiased if it averages at true population parameters
with repeated sampling:
Suppose θ is an estimator for the true population parameter θ. It is called unbiased if
E (θ) = θ. If this is...
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This note was uploaded on 03/17/2014 for the course ECON 404 taught by Professor Staff during the Spring '08 term at University of Michigan.
- Spring '08