3. (10 points) Suppose we randomly select 5 students from STAT3025. Let X, . No denote their grades on the first quiz, and Y), Y denote the grades on the second quiz. Assume X, ~ N(th. ";) and Y. ~ N(ja. 1 2 3 4 5 61 62 56 70 63 70 52 78 74 70 (a) (3 points) Since these are dependent samples, what is the most appropriate estimator of 8 = /1 - #2 Find its value in the case of the above data. Also, find the value of the estimator for the variance of & given usually by ". (b) (7 points) Construct the Paired two sample I-test at a = 0.05 for Ho po =0 vs. H. Up