We have two group of people (one of $n$ people, the other of $m$ people) that go through the same entertainment experience (think about a day at the amusement park or something like that).
One group gets a special treatment over the other group at some moment during the day (a free drink for example). At the end of the day, each participant gives a satisfaction grade (an integer) $X_1, \cdots, X_n, Y_1, \cdots, Y_m$ that ranges from $0$ to $5$.
We would like to know if the special treatment affects the overall satisfaction of the experience.
I guess that we have to test if the means of the satisfaction of the two groups are equal ? What test should be used ?