The table at the bottom of the page shows how the history

Question

The table at the bottom of the page shows how the history and economics scores of 25 students are distributed. Use the method of Exercise 32 to determine the value of r, replacing the row headings by the corresponding class marks (midpoints) 23, 28, 33, 38, 43, and 48 and the column headings by the corresponding class marks 23, 28, 33, 38, and 43. Use this value of r to test at the 0.05 level of significance whether there is a relationship between scores in the two subjects.

Exercise 32

In a random sample of n pairs of values of X and Y, (x_i, y_j) occurs _ij times for i = 1, 2, ... ,r and j = 1, 2, ... , c. Letting_i· denote the number of pairs where X takes on the value x_i and _·j the number of pairs where Y takes on the value y_j, write a formula for the coefficient of correlation.