SECTION 6.1 Summary

• The sample mean of an SRS of size drawn from a large population with mean and standard deviation has a sampling distribution with mean and standard deviation
  

• The sample mean is an unbiased estimator of the population mean and is less variable than a single observation. The standard deviation decreases in proportion to the square root of the sample size . This means that to reduce the standard deviation by a factor of , we need to increase the sample size by a factor of .
• The central limit theorem states that for large the sampling distribution of is approximately for any population with mean and finite standard deviation . This allows us to approximate probability calculations of using the Normal distribution.