Answer to Question #330104 in Statistics and Probability for SAM

Question

1.     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 worst than the actual grade, as shown in the following table:

 

Predicted grade

Actual

Grade Obtained

 

Better

Equal

Worst

 

B

16

30

12

58

C

10

20

9

39

D

20

15

18

53

 

46

65

39

150

 

Carry out a χ² test at the 5% level of significance to determine whether the teachers prediction and the actual results are independent.