I have a question on solution 1 to Simpson's Paradox. It says using paired t-test to compare Day 1 control vs treatment and Day 2 control vs treatment. But paired t-test is used when the two groups are related, usually the same group before and after treatment. If looking at control and treatment on the same day, the groups are often unrelated and thus use unpaired t-test. Also does solution one suggest that we should conclude that treatment won because we are not looking at the aggregate? Thank you in advance for any clarification, just want to understand the first solution better.