Statistical Sciences 2244A/B Lecture Notes - Lecture 12: Bias Of An Estimator, Sampling Distribution, Standard Deviation
13 Apr 2018
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Document Summary
P hat - p hat estimates the di erence between p1 and p2. When two random variables are normally distributed, the new variable di erence also follows a normal distribution centred on the di erence between the two variables" means and with variance equal to the sum of the two variables" variances. When the two samples are large, the distribution of p hat - p hat is approximately normal. The mean of the sampling distribution is p1 - p2 (di erence between sample proportions that is an unbiased estimator of the di erence between population proportions. Srs of size n1 from a large population having proportion p1 of successes and an independent srs of size n2 from another large population having proportion p2 of successes. When n1 and n2 are large, the con dence interval for p1 - p2 is (p hat1 - p hat2) +- z*se.
