Since the graduate student knows the standard deviation of the scores on the psychotic symptoms inventory for the population of people who are psychotic, she intends to use a hypothesis test that uses the z-score of the sample mean as the test statistic (also known as the z test). First, she wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test?
Each observation is independent of every other observation.
Members of the sample are selected randomly.
Each member of the sample must be related in some way to at least one other member of the sample (as in a sibling, friend, or coworker).
The scores on the psychotic symptoms inventory follow a normal distribution or the sample size is large (at least 30).
The standard deviation of the scores on the psychotic symptoms inventory is the same for those who take the antipsychotic and those who don’t.