CENTRAL LIMIT THEOREM HANDOUT

CENTRAL LIMIT THEOREM HANDOUT

SYMBOLS

s

sample standard deviation

s2 sample variance σ population standard deviation σ2 population variance ρµ population proportion ρs sample proportion µ population mean 0

sample mean

µ0 mean of a sampling distribution of means σ0 standard deviation (standard error) of a sampling distribution of means µp mean of a sampling distribution of proportions σp standard deviation (standard error) of a sampling distribution of proportions

CENTRAL LIMIT THEOREM If repeated random sample of size N are drawn from a normally distributed population (variable) with a mean (µ) and a standard deviation (σ) the resulting sampling distribution will be normal in shape with a mean (µ0) = µ and a standard deviation (or standard error) σ0 = σ/√Ν