Chapter 7: The Central limit Theorem

Formula needed to make sample size "normal"

Converting SD: Standard Deviation ----------------- square root of x( sample size) MEAN=THE SAME

How to use the Central Limit Theorem?

When question does not state that it is normally distributed

Assessing normality

- if sample is not bell shaped , you cannot make it normal or approx normal If the distribution is normal, its histogram will be normal shaped, which is a bell shape that is symmetrical about the mean. You should not see features such as skewness, gaps, outliers, or clusters; these are not considered normal. - construct a histogram to see if it is bell shaped 1. min , max and number of classes 2. find width: max- min ------------ sample of classes 3.construct classes and frequency 4. construct histogram

Steps to solve a problem that is not normally distributed and also has a sample size over 30

1. note that it is not normally distributed 2.make sure sample size is over 30 3.Force mean and SD to be normal by using formula 4.convert that sample size to a z-score 5.if question says "greater than", subtract answer by 1

The central limit theorem

The central limit theorem states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough. -sample size has to be greater than 30

Why use the Central Limit Theorem?

To identify characteristics of a sampling distribution and also to transfer the problem to become a "normally distributed" problem