I am doing a simple study that involved taking a measure at time point 1 and 12 weeks later, time point 2. While the sample was a class, not all members were present at both time points, so I have 20 date points at time 1 and 21 date points at time 2. The measure has a score, and I am taking the means and doing a simple t-test to determine if the intervention caused any increase in the measure at time point 2.

Questions: Do I throw out outliers if they are more than 2 std deviations higher than the mean?

When I do the t-test, do I need 1 or 2 tailed distributions? My hypothesis is that the intervention will increase the mean at time 2, so I think I should do a 1 tailed distribution.

Lastly, I am assuming that I do a paired t-test since it is a repeated measures design.