The Distribution of Sample Means

Standard Normal Distribution is a normal distribution that has been

converted into Z-scores

Standard Normal Distribution has a mean (μ) of

0

Standard Normal Distribution has a SD (σ) of

1

Distribution of Sample Means is the distribution form by

all possible sample means of size n

Distribution of Sample Means shows how sample mean

cluster around the population mean

Distribution of Sample Means is approximately

normal in shape

the larger the sample size, the closer the

sample means (M) will be to the population mean (μ)

the larger the sample size, the smaller

the sample error (standard error)

The mean of the distribution of sample mean (μM) is

equal to the mean of the population mean (μ)

The name of the mean of the distribution of sample mean (μM) is

Expected value of M

Standard Error is

SD distribution of sample mean [ σM ]

SD of sample mean is

how far off our sample mean is likely to be from the population mean

you want the SD to get

as close to 0 as possible

less variability (as close to 0) means

your sample mean is closer to the true population mean

The sampling error is

the difference between a sample statistic and the corresponding population parameter

Central Limit Theorem is when

as sample size (n) approaches infinity, the sample mean distribution will form a normal distribution even if the original population isn’t normal

finding z-score using sample mean

use M instead of X in the equation and use standard error instead of SD