1. Consider a model given by Yij = #z' + 853' for 2' : 1,...,'r and j : 1,...,n,, where [.L, E R are constants and 5,,- are in- dependent and identically distributed random variables distributed according to Student's t-distribution with 1/ > 2 degrees of freedom. We have that E63,,- : 0 and Vare,,- : V/(V 2) since V > 2. (a) (2 points) Does the assumption of normality hold for this model? Include an explanation. (b) (2 points) Does the assumption of equal variances hold for this model? Include an explanation. (c) (2 points) Suppose that we observe the responses Y,,- with 2' 1,. ,r and j 1,. ,n, and our goal 18 to estimate the treatment means it,- using the estimator Y-. 71,71 Z}; 1 Y,-,. Is it true that E17,: 11,- (i. e. is the estimator unbiased). Include an explanation. (d) (1 point) Obtain an expression of the variance of the estimator Y, in terms of n,- and 1/ (it has to be an expression that only contains 11,: and u). (e) (2 points) Consider the condence interval with the bounds given by Y, :I: z(1 05/2) X 307,), where 21(1 a / 2) is the quantile of the standard normal distribution and 307,.) is the estimator of the standard error of Y,\" When and why can we justify the use of this condence interval