Question

The scores of 7 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 93 Bailey 98 96 Cruz 95 80 DeSana 93 75 Erickson 89 99 Francis 80 83 Gray 71 95 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary Test statistiers

Answer 1

exam 2 93 98 1.5 - 2.5 -6. 25 १४ Barley 90 1.5 4 -3 4 89 80 6 83 3 71 pe 7 Suppose that the scores of 7 students on the midterm and final are given as follows: student Midterm Rank 1 Fipal Rank 2 di di Anderson 4 98 96 0.25 couz 95 6 - 3 9 pesana 93 75 a Erickson pa 16 Francis 5 95 4 16 Total 57.5 + To calculate spearman's Rank correlation coefficient, we first rank the midterm and final scores seperately and take difference of ranks studenti per → When there is te in hanks then, we take aruage of the top tied ranks. The Spearman's Rank correlation Coefficient is given by 6 @ do Lg= 1- 6692-1) where di is difference in ranks for ith stadent, nis number of Stadents. 131 -0.0 Q68. - as = 1 6 x 57.5 7 (71) To test whether there is correlation between midteem and final scores, the hypothests are: Ho: The population Spearman's Rank correlation , P = 0 versus He: The population Specimao's Kante correlation, P to

- use for no10, we use fatest to test for e=o. Here, n<lo. Hence we rs value as test statistic and the critical value is obtained from Spearman's table. For n=6, a=0.05 and two-tailed. 4. PC, 0.025) = 0.886. Since, Rs > PC6,0.025) , we do not reject Ho and conclude that there is no correlation between midterm scores and final escam score. and &sc PC6,0.025)
From the above results we can say that there is no correlation between mid term and final scores.