a. About half of New Hampshire residents get their drinking water from private wells. You want to investigate whether people who get their drinking water from private wells are more likely to get sick than those that don't. Let ;; be the number of days a person is ill during 2023 if they get their drinking water from private wells, and Y}, if they don't; Let T; be a dummy equal to 1 if person i actually does get their drinking water from private wells, 0 otherwise. i. Insymbols, write down the estimator that compares the average number of sick days of those who drink from private wells to those who don't. ii. In symbols, what do you need to be true for the estimator in part (i) to be the causal effect of private well water on sick days? iii. Say (ii) in words