The percent of people with lactose intolerance ranges from a low of 4% in Ireland to a high of 100% in countries several countries including South Korea and Malawi. A researcher in Ohio wanted to estimate the proportion of lactose intolerant adults in Ohio. He took a random sample of 150 adults in Ohio and found that 56 were lactose intolerant. Required:
Use these data to construct and interpret a 90% confidence interval about the proportion adults in Ohio who are lactose intolerant.

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) ).