A proper statistical test needed!

Dear my friends,
I am a computer science student, and I have a set of data. My data is divided in two groups (size of each group: n1=3928 and n2=26). Each element of these groups has one specific score and scores of each group have been normalized with a min-max normalization (min=0, max=1).
I need a statistical test which proves that one specific value, for example 0.4, can separate these two groups.
I used t-test; however, I am not sure I have applied it correctly (and I am not sure that the t-test is a suitable one or not).
Any help is really appreciated


Ambassador to the humans
I'm not sure you'll be able to find anything that "proves" that a certain value splits the data perfectly because most likely there isn't such a value. I second the discriminant analysis suggestion though. That will give you the best value to split the data. Note this doesn't "prove" that if one observation is to the left of the value then it's in group A and to the right it's in group B. It just gives you a best guess.