ECON 2B03 Lecture Notes - Lecture 13: Central Limit Theorem, 12012, Standard Score
19 Jan 2014
School
Department
Course
Professor
Document Summary
The central limit theorem is one of the most important theorems in statistics, and is the principal reason why normal distribution is the most important of all probability distribution. Suppose that weekly food expenditures of mcmaster students are drawn from a distribution having = =. Suppose we take a random sample of 100 students and calculate probability that. X has an approximately normal distribution with a mean of and variance of . 44 (var ( x )= 2 n. Next, obtain the probabilities from the standard normal distribution. Therefore p( x )= p( 0. 83 z 0. 83)= p( z 0. 83) p( z 0. 83 )=0. 7967 0. 2033=0. 5934. If we took a sample size of 100, the probability is 59% that our sample mean would be within of the unknow population mean. In r we would compute this as follows: pnorm(0. 83) pnorm(-0. 83) The distribution of the difference between sample means.
