A professor in the psychology department would like to deter

A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department had 12% As, 24% Bs, 36% Cs, 18% Ds, and 10% Fs. A sample of n = 200 psychology students from last semester produced the following grade distribution.

Do the data indicate a significant change in the grade distribution? Test at the 0.05 level of significance. (Round your answers to two decimal places.)

Conclusion

a. Fail to reject the null hypothesis. There is evidence that the grading distribution has changed.

b. Fail to reject the null hypothesis. There is not evidence that the grading distribution has changed.    

c. Reject the null hypothesis. There is not evidence that the grading distribution has changed.

d. Reject the null hypothesis. There is evidence that the grading distribution has changed.

Solution

Constructing an expected value table,

   Observed   Expected
A   31   24
B   62   48
C   67   72
D   28   36
F   12   20

As

df = a - 1 = 5 - 1 = 4,

chi^2(crit) = 9.487729037 [ANSWER]

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Using

chi^2 = Sum[(O - E)^2/E]

Then

chi^2 = 11.45 [ANSWER]

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As chi^2 > chi^2(crit), then:

OPTION D: Reject the null hypothesis. There is evidence that the grading distribution has changed. [ANSWER]