The following assumptions are required to hold in order for a #z#-test to produce valid conclusions:

• Random sampling

The process of inferential statistics heavily relies on the assumption that the sample being analyzed is representative of the larger population it is drawn from. Random sampling helps ensure the representativeness of the sample.

• Independent observations

Two observations are said to be independent when the occurrence of one observation does not influence the chances of the second observation occurring.

• The value of #\sigma# is unchanged by the treatment

When testing for a treatment effect, it is assumed that the amount of variability in the treated population is equal to the amount of variability in the untreated population.

• Normal sampling distribution

When conducting a #Z#-test the Standard Normal Table is used to determine the boundaries of the critical region. This table can only be used when the central limit theorem holds and the distribution of sample means is normal.