Research Methods Module 3: The Distribution of Sample Means

MBB2

One population has a lot of sample to choose from so to resolve the problem we need

a score for our one sample and that would be the mean sample then we need a distribution made up of sample means within which we could examine our one sample mean

The distribution of sample means

• is made up of the sample means from all of the random samples of a certain size (n) that could possibly be obtained from a pollution

• governed by a mathematical theorem the central limit theorem

Central limit theorem

• tells us the precise characteristics of the distribution of any distribution of sample means of any size

• mean of the distribution is the same as the population mean

• For large sample sizes (30 or more), the distribution of sample means will have a normal shape

• the standard deviation of the distribution of sample means which is called “Standard Error”

Standard error formula

• as sample size increases standard error decreases. In turn, estimation of the population mean becomes more precise. When a sample is large enough, its mean provides a reliable estimate of the population mean

What does all this mean

• if the sample is large enough the sample means will be normal

• we can calculate standard error and we know what the mean of the distribution of sample means

• thus, we can use our 2s rule of thumb to test if our sample mean is typical or if it is extreme