I have a simple experiment with two groups of subjects (each group has $30$ subjects). At the outset of the study, the two groups have shown to be equal in terms of the dependent variable. Now we introduce a treatment to one of the groups, keeping the second group as the control group.
1- To measure the efficacy of the treatment, should I only run one independent samples t-test between the treatment and experimental groups?
2- Suppose the two groups were not equal at the outset of the study. What design I could employ to measure the efficacy of the treatment in these two groups?