24.1. The expected count of students with average grades of A and B who have played games is

24.2. To find the chi-square statistic, we add six terms for the six cells in the two-way table:

24.3. To assess the statistical significance, we begin by noting that the two-way table has two rows and two columns. That is, r = 2 and c = 2. The chi-square statistic therefore has degrees of freedom

(r − 1)(c −1) = (2 − 1)(2 − 1) = (1)(1) = 1

Look in the df = 1 row of Table 24.1. We see that X² = 6.74 is larger than the critical value 3.84 required for significance at the α = 0.05 level. The study shows a significant relationship (P < 0.05) between playing games and average grades.