1. You developed an intervention to improve children's self-efficacy. You conducted a randomized trial to evaluate your intervention, in which third graders were randomly assigned to receive your intervention or not (a control group). The tool you used to measure children's self-efficacy gives a score of 0-60, with higher scores indicating greater self-efficacy. You also collected data on whether children were eligible for free or reduced-price meals at school, which indicates a lower socioeconomic status and potentially other stressors in a child's life. These are the average scores, disaggregated by treatment arm and eligibility for free/reduced-price meals: Eligible for free/ reduced-price meal? Yes No Treatment Intervention Control 36 30 46 35 You fit the following statistical model to the data: Yijk = l + Ti + j + (TB) ij + Eijk, where Xijk is a child's self-efficacy score (the kth child in treatment i with eligibility status j), is the average self-efficacy score among children in this population, t is effect of treatment i, j is the effect of eligibility status for free/reduced-price meals (indexed by j), (t) is the interaction effect of treatment i and eligibility status j, and ijk is the random error term. You find that there is a statistically significant interaction between treatment and eligibility status.