The mayor of Gemelos, CA strongly believes that drinking coffee stunts growth. In an attempt to getcoffee banned from Gemelos, the mayor gathers the 43 pairs of young (under the age of 18) identicaltwins living in Gemelos. For the course of five months he requires one twin to drink coffee and the otherto abstain from coffee drinking. Then the mayor records the height of each twin.

Is this a matched pairs design? Justify.

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).