Quest ion 5 Suppose we want to assess the effectiveness of a short course on nutrition. Eight st were given a test before and after taking a short course on nutrition. The data are below. Student Before After Improvement 50 56 6 71 78 7 87 100 13 75 71 4 82 95 13 91 96 5 63 79 16 80 84 4 GDHJCDUII-F-WMH a) Please explain why the above sample observations are treated as matched pair (dept samples instead of independent samples. b) . B A Let the 1\"11 student's before (B) and after (A) score be denoted as :rE ) and mg ). Also, let 6;- denotes the i"11 student's score di'erence 3 61; = my) mg\") Suppose we are interested in an interval estimation for population mean difference #5. Assuming the dilfcrcnces are normally distributed, please construct a 95% condence interval for m. You may use ZTestO or t.test() to verify your answer, but replicate the values mathematically yourself and show your work as well