A survey was carried out with students that had studied Maths, Physics and Chemistry at a college between 2016 and 2020. The students were divided into two groups $$\(A\)$$ and $$\(B\)$$. Test, at the 5\% level of significance, whether the subject enjoyed the most is independent of group. You should state your hypotheses, expected frequencies, test statistic and the critical value used for this test. (8) The Headteacher discovered later that the results were actually based on a random sample of 200 students but had been recorded in the table as percentages.

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