I think that you first have to set up your null and alternative hypothesis, specify what kind of data you are facing and then select the test.
The t test requires that the data is normally distributed. In particular this means that any outcome between minus infinity and plus infinity is possible.
The t test can also be applied if you believe that the sample is sufficiently large. However you cannot prove that it is large, in particular there is no number that one can specify a priori.
Long story short, the t test does not seem appropriate.
Instead I would use the Wilcoxon test. Note however that this test can only determine that there was an effect. If you use the same people in both treatments you have to use the version for matched pairs.