Question: Identify three characteristics of the sampling distribution of the sample mean; calculate the mean and standard error of a sampling distribution of the sample mean and draw the shape of this distribution.

• The sample mean has the following three characteristics:

a. The sample mean is an unbiased estimator. On average, the sample mean we obtain in a randomly selected sample will equal the value of the population mean.

b. A distribution of sample means follows the central limit theorem. Regardless of the shape of the distribution in a population, the distribution of sample means selected at random from the population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases.

c. A distribution of sample means has minimum variance. The sampling distribution of the mean will vary minimally from the value of the population mean.