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 selected sample is representative of the population it is drawn from. Using a random sampling method helps to 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. An important mechanism by which independence is violated occurs with small populations if you sample without replacement. Then one observation will influence the remaining observations that can occur. As a general guideline you may assume that observations are independent if the population is at least #10# times as big as your sample.

• Normal sampling distribution

In order for a #z#-test to produce valid results, the sampling distribution of the #z#-statistic has to be (approximately) normally distributed.