STT 212 Lecture Notes - Lecture 13: Central Limit Theorem, Sampling Distribution, Standard Deviation

• School: University of Rochester
• Department: Statistics
• Course: STT 212
• Professor: Mcdermott

Document Summary

Let"s get more specific about the normality features of the central limit theorem. Normal distributions have two parameters , the mean and standard deviation. As the sample size increases, the sampling distribution converges on a normal distribution where the mean equals the population mean, and the standard deviation equals / n. As the sample size (n) increases, the standard deviation of the sampling distribution becomes smaller because the square root of the sample size is in the denominator. In other words, the sampling distribution clusters more tightly around the mean as sample size increases. As sample size increases, the sampling distribution more closely approximates the normal distribution, and the spread of that distribution tightens. These properties have essential implications in statistics that i"ll discuss later in this post. There is a mathematical proof for the central theorem, but that is beyond the scope of this blog post. However, i will show how it works empirically by using statistical simulation software.