The Director of Studies at a large college believed that students' grades in Mathematics were independent of their grades in English. She examined the results of a random group of candidates who had studied both subjects and she recorded the number of candidates in each of the 6 categories shown.
Maths grade A or B
Maths grade C or D
Maths grade E or U
English grade A or B
25
25
10
English grade C to U
15
30
15
Stating your hypotheses clearly, test the Director's belief using a \(10 \%\) level of significance. You must show each step of your working.
The Head of English suggested that the Director was losing accuracy by combining the English grades C to U in one row. He suggested that the Director should split the English grades into two rows, grades C or D and grades E or U as for Mathematics.
State why this might lead to problems in performing the test.