Remark: The Z-test hinges on the requirements,

1. the distribution of the population (data) is normal.

2. the standard deviation, σ, is known.

*If the distribution is normal, then our test is an exact test.

**If the distribution of the data is not normal, but the sample size is large, then by the CLT, is approximately normal and our test result will be approximate.

*** If the distribution in not normal and the sample size is small, then we cannot use the test.