The sampling distribution of z must be normally distributed to use the z test.

Question

Quizplus · Accepted Answer

The z test is based on the assumption that the sampling distribution of the mean is normally distributed. When the sample size is large (n > 30), the central limit theorem states that the sampling distribution of the mean will be approximately normal, even if the underlying population is not. Therefore, it is safe to use the z test in this case. However, if the sample size is small (n < 30) and the population is not normally distributed, the t test should be used instead.

The Sampling Distribution of Z Must Be Normally Distributed to Use