POLS 3650 Lecture Notes - Lecture 9: Central Limit Theorem, Statistical Inference, Univariate Analysis
8 Feb 2018
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Document Summary
The mean of the sampling distribution will be identical to the true population mean. This applies even if the variable itself is not normally distributed. Since we know this is true, we can calculate the probability of finding point estimates that are far away from the parameter value. If we were to draw thousands of random samples, calculate the mean for each sample, and visualize all sample means, we would end up with a normal distribution centered around the population mean (clt) 95 percent of these thousands of samples would have a mean that is two standard deviations on the sampling distributions away from the population mean. If we draw one sample, we have a 95 percent chance of finding a mean that is two standard deviations on the sampling distribution away from the population mean. The more spread out the sampling distribution the confidence interval will be much wider.
