I don't have much background in statistics, and one of the exercises in my programming course asks for the following:
- Generate a sample of normally distributed data using rejection sampling and Metropolis (I did this).
- Check, using appropriate statistical tests, if the results agree with a normal distribution.
My background in practical statistics is fairly limited, so I'm not sure what is meant by appropriate statistical tests. I'm guessing there are tests designed especially for checking if a sample is from a normal distribution with a given $\mu, \sigma$ (I'm generating the sample with fixed values of the parameters).
Also, I would like to try randomizing the $\mu, \sigma$ values, and then use some test for checking whether the data are from any normal distribution (I'm guessing there's a test for that, and that it's different from the previous one).
Which tests should I use and how to use them?