Sampling Distribution (Model for a Mean)

A sampling distribution is a model that describes the probability of a sample statistic, such as a mean, by simulating data from a population many times. A sampling distribution is constructed by drawing a large number of randomly selected samples of the same size from a population and then calculating the mean of each sample. This creates a distribution of means where the most likely mean is the population mean. The shape of the sampling distribution depends on the shape of the population distribution and the size of the samples. As the sample size increases, the sampling distribution becomes more narrow and peaks closer to the population mean.

If assumptions of independence and random sampling are met, and the sample size is large enough, the ____________ of the sample mean is modeled by a Normal model with a mean equal to the population mean, and a standard deviation equal to