Answer to Question #209975 in Statistics and Probability for Scott Kabiro

Question

  At a professional examination students were getting grades A, B, C, D and E in the ration of 1:3:4:5:7 In the last examination 600 students who took the revision block release classes, were graded as follows:

Grade

A

B

C

D

E

Number of Students

50

100

130

150

170

 

By using the Chi Square, check if there is an improvement in student’s performance after taking revision block release classes at 0.05 level of significance and advice the examination board?

Answer 1

Let Null Hypothesis,

$H_o:$ The claim is true that there is an improvement in student’s performance after taking revision block release classes.

and $H_a:$ The claim is not true

n=600,

Ratio of A,B,C,D and E= 1:3:4:5:7

Expected frequency = 30,90,120,150,210

The table for chi-square is-

So, $\chi^2=\sum \dfrac{(OB-E)^2}{E}=22.89683$

The standard value of $\chi^2$ at $\alpha=0.05$ , and Degree of freedom dof=(n-1)=(5-1)=4 is 9.488

Conclusion: As The calculated value of $\chi^2$ is more than the Standard value, So Null hypothesis $H_o$ is rejected i.e.   The claim is not true that there is an improvement in student’s performance after taking revision block release classes.