I only completed one statistics class yet and now struggle with my first project involving statistics.

I want to conduct an evaluation where items are rated according to particular scales, leading to a lot of probability distributions, where there is one distribution for each item, scale and several users.

In order to limit the amount of participants required in the evaluation, I am looking for a test which is able to determine a normal distribution with a certain alpha=0.05 and only requires very little sample sizes while still having a high accuracy. I would prefer sample sizes as little as <=10. Given the fact that I have to implement the test in c#, a ranked list of available tests would be of great benefit. The only test I know and tried yet is the \chi^2 one.

Thank you so much for your help!

Christian