In the past, of all students enrolled in Principles of Microeconomics (ECON 222)

Question

In the past, of all students enrolled in Principles of Microeconomics (ECON 222) 12% earned A's 18% earned B's, 30% earned C's, 20% earned D's, and the rest received F's or withdrew. The chair of the Department of Economics is concerned that there is grade inflation in this class. The grade distribution of the current class of 60 students taking ECON 222 is as follows: 10 A's, 20 B's, 20 C's, 5 D's, and 5 F's or W's. Assuming that this class constitutes a random sample, is there any evidence that the grade distribution has changed at alpha = .05? What would you conclude about the change of grade distribution and chair's concern about the possible grade inflation?

Explanation / Answer

The problem deals with enrolled students in Micro Economics. There are 60 students in the class. As per grade distribution, 10 students should get grade A, 20 students gradeB, 20 again in grade C, 5 in grade D and also 5 students in grade F.

But actual result shows that 12% have secured Grade A, 18% grade B, 30% Grade C, 20% Grade D and rest 20% grade F.

You have to justify that whether there is any evidence of change in grade. It can be carried out by usig statistical test known as Chi-square. It requires-

1. At leat 50 observatios in the sample. Here number of student is 60.

2. Data must be expressed in original units. You can get it by multiplying 60 students with percentages.

3. At least there will be five groups. Here you are getting 5 groups A,B,C,D and F

Next consider null hypothesis. It is the believe that is available unless otherwise proved . Thus

N0: No change in grade.

In order to do chi-sqare test following table has been prepared.

From table, calculated chi-sqare value is 24.4. You have to compare it with table value. For ascetaining table value you require degree of freedom. It is number of groups-1. So it is 5-1=4 indicated by v. Now consider critical value alpha. It is 0.05. So you require 95% accuracy in your decision. From table chi-square value of v=4 and alpha 0.05 is 9.488. Calculated chisqare value is higher than the table value. So null hypothesis is rejected.

Answer: Grade has change. There is grade inflation.

Grade Actual(O) Expected(E) O-E (O-E)2 (O-E)2/E A 60x12%=7 10 7-10=-3 9 9/10=0.9 B 60x18%=11 20 11-20=9 81 81/20=4.0 C 60x30%=18 20 18-20=-2 4 4/20=0.2 D 60x20%=12 5 12-5=7 49 49/5=9.8 F 60x20%=12 5 12-5=7 49 49/5=9.8 Total 24.4

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