Answer to Question #174619 in Statistics and Probability for denuwan

Question

Grades assigned by an economics lecturer for his postgraduate coursework students at a SLIIT have historically followed a symmetrical distribution: 5% HDs, 25% Ds, 40% Cs, 25% Ps and 5% Fs. This year, a sample of grades revealed 11 HDs, 32 Ds, 62 Cs, 29 Ps and 16 Fs. Can you conclude, at the 1% level of significance, that this year’s marks are distributed differently from marks in the past?

Answer 1

Let $H_o$ : This year’s marks are distributed differently from marks in the past.

The dstribution is as follows-

Expected frequency represented by $E_i$

So The value of $\chi^2=\sum \dfrac{(O_i-E_i)^2}{E_i}=15.12$

The tabulated value of $\chi^2$ at 1% level of significance is 13.28

Conclusion: As the calculated value of $\chi^2$ is greater than tabulated value So $H_o$ is rejected

means This year’s marks are distributed differently from marks in the past.