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Unformatted text preview: ple mean? See the problem set question) 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 <Z < ) 0.04 0.04 = 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: Unbiasedness 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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