Five students have compared their scores in some practice papers that they sat before their exam. Their marks were as follows: Student 1 72, 75, 62, 71, 60, 59 Student 2 78, 82, 64, 72 Student 3 90, 78, 67, 71, 83 Student 4 80, 77, 76, 81, 64 Student 5 95, 88, 62 Consider the model: Y =Uttiten i =1,2,3,4,5 j=1,2, ...,n; e;; ~ N(0,02) where ya; is the score of the ith student on the j th practice paper and n; is the number of papers taken by student i. The ey are independent and identically distributed and Enit; = 0. (1) Calculate the least squares estimates of / and 7;, i =1.2,3,4,5. (ii) Perform an analysis of variance on these results stating clearly the null hypothesis and your conclusion. (iii) Calculate a 95% confidence interval for the underlying common standard deviation for all students assuming that the null hypothesis holds true.(@) Assume the following information represents the National Income model of an Utopian' economy. Y = C+I+G C=atb( Y-T) T=d+tY I= I. G = Go Where a >0; 0 0;0