A mathematics placement test is given to all entering freshmen at a small college. A student who receives a grade below 35 is denied admission to the regular mathematics course and placed in a remedial class. The placement test scores (x) and the final course grades (y) for 20 students who took the regular course were recorded. A scatterplot of these data is given below:
The following computed quantities are provided:
å x = 1110 à y = 1173 å xy = 67,690 å x2 = 67,100 ảy = 74,725
(a) Calculate the value of the correlation coefficient using the computing formulas for S Syy, and Sy. Does your answer seem reasonable based on the pattern of points displayed in the scatterplot? (5 points)
(b) Test the hypothesis H, :p=0 (No correlation) versus H: #0 (Correlation) at the 5% level of significance using the t test statistic. What is your conclusion? (5 points)
(c) Test the same hypothesis at the a=0.05 level using the value of r and Table A-6. Is your conclusion the same as in part (b)? (5 points) (d) Compute the value ofr and interpret it. (5 points)