Question

Question 2 The following table shows the mathscore (x) and grade (v) obtained by 10 students in one local institution in Gaborone. Student Number Grade (v) Mathscore (x) x*y 65 39 2 535 52 59.816-57760 Von WN -- 47 28 75 34 3354 1 092 5248 5244 4 183 2044 7350 1 904 3 900 36 854 4 225 6 084 2 704 6724 8 464 7921 5329 9 604 3136 5 625 59 816 1521 1849 441 4096 3249 2209 784 5625 1156 2704 23634 52 Total 460 yoy-41 Page 1 of 2 n 6-6 a) Draw a scatter diagram and comment on the nature of relationship between the Mathscore and Grade obtained by the ten students. b) Fit a linear regression of the Grade (y) on Mathscore (x). c) Construct an analysis of variance (ANOVA) table and test at 5% level of significance and make the necessary conclusions. What is the estimated error variance d) Obtain the point estimate of the mean grade when the Mathscore is 60 and its corresponding 95% confidence interval e) Suppose we want to test the null hypothesis that the correlation coefficient, p=0.5. Calculate the sample correlation coefficient and construct the 95% confidence interval for p, and conclude. [5+12+12+8+13=50 Marks]