Before students wrote a mathematics examination, their teacher had made predictions about the results that students will receive. After the actual results of the examinations, the results for 150 candidates were classified according to whether the predicted grade was better than, equal to, or worse than the actual grade, as shown in the following table:   Predicted grade Actual Grade Obtained   Better Equal Worst   B 17 30 12 59 C 10 22 9 41 D 20 15 15 50   47 67 36 150   Carry out a χ2 test at the 5% level of significance to determine whether the teachers prediction and the actual results are independent

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