# OMIS 2010 Chapter Notes -Sampling Distribution, Standard Error, Central Limit Theorem

## Document Summary

Is created by sampling draw sample of same size from a population or use rules of probability and laws of expected value and variance to derive sampling distribution. Variance of sampling distribution of sample mean is variance of population divided by sample size. Standard error of the mean: standard deviation of sampling distribution, for infinitely large populations. As # of throws of the die increases, probability that sample mean will be close to population mean increases: sampling distribution of x bar becomes narrower as n increases; sampling distribution becomes increasingly bell-shaped. Note: if population id normal then x bar is normally distributed for all values of n if population is non-normal then x bar is normal for only larger values of n. If population extremely non-normal (bimodal/highly skewed distribution) sampling distribution will also be non-normal even for large values of n . If population is finite, the standard error need to use different approach.