A Z-test assumes the data is normally distributed which according to the central limit theorem is when the sample size is large, usually when n > 30. You use the Z-test for e means when you want to see if there is any different between the means of two normally distributed samples.
One sample Z test is used to test whether the mean of a population is less than, greater than or equal to a specific value μ.
Example, Morel suspects there are less than 210 candies in an M&Ms bag. Morel buys 60 M&Ms bags and count all the candies in each bag. After some calculations Morel found out the mean value were 203 M&Ms in each bag and the variance was 10. What is the p-value of this test? Was Morel right is there less than 210 M&Ms in the bag?
H0: There is 210 M&Ms in each bag
H1: There is less than 210 M&Ms in each bag