Arandom sample of 49 measurements from a population with population standard deviation σ1 = 4 had a sample mean of x1 = 9. an independent random sample of 64 measurements from a second population with population standard deviation σ2 = 5 had a sample mean of x2 = 12. test the claim that the population means are different. use level of significance 0.01. find a 99% confidence interval for μ1 − μ2.

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) ).