Question

STATS! Conditions to use the Z-test? ... I know it has something to do with the central limit theorem – does the sample population have to be normally distributed OR does the actual population have to be normally distributed...?

In the problem I'm working with, I have to do a z-test for the difference between means of sample A and B... I have a data table of the scores but I'm not sure how to explain the conditions of using a z-test...

Answer 1

Just a bit of background info....
Two mouthwash treatments were tested. The first, labelled A, was a standard product in common use, while the second, labelled B, was a new preparation. The volunteers then entered a program that lasted for four weeks. Eight of the volunteers were given mouthwash A first, in days 2-7, and then mouthwash B second, for days 23-28.

The other eight volunteers were given mouthwash B first and then mouthwash A second.

During the whole experiment, the subjects used their normal teeth cleaning routine, supplemented by the respective mouthwashes in the two experimental periods.

At the end of each period, the dental student examined the teeth of each subject, giving each tooth a score between 0 and 4 according to the amount of plaque, a score of 4 representing the highest level of plaque and 0 the least.

An average value was then calculated for each subject when using each mouthwash.
The average scores were called Score A (referring to mouthwash A) and Score B (referring to mouthwash B).