Elementary Statistics – Clarification about Z-values

Recall the general formula (based on a population of individual values) for a z-value: . This is the standardization you use when working with an individual normal variable (not a sample).

In the context of a significance test for a population mean (where the population standard deviation is known), we use a very specific z-value as our test statistic: . This test statistic is listed on your exam formula sheet. Please, do not assume this is the new z-value you always use. This is used in the specific case of a significance test for the population mean.

Note we now have four statistics () that have approximate normal distributions under certain circumstances.

Be sure to standardize your statistic with its appropriate mean and standard deviation:

· z-value when dealing with a sample count of successes:

· z-value when dealing with a sample proportion of successes:

· z-value when dealing with a sample mean:

· z-value when dealing with a sample total: