A sample of final exam grades for n = 500 students was analyzed. The assumptions

Question

A sample of final exam grades for n = 500 students was analyzed. The assumptions expressed in terms of theoretical proportions are listed below P [A] = 0.10, P [B] = 0.30, P[C] = 0.40, P [D] = 016, and P [F] = 0.04. The observed frequencies were such that 60 students earned "A" grades, 174 students earned "B" grades, 180 students were graded with a "C", 62 students ended up with "D" grades, and 24 students failed the final exam. 1. Evaluate the X^2 statistic for the goodness-of-fit test. Test Statistic = 2. At the significance level of alpha = 5%, do data provide evidence that the grade distribution significantly differs from the theoretical projection? At the significance level of alpha = 1%, do data provide evidence that the grade distribution significantly differs from the theoretical projection?

Explanation / Answer

from above Chi stat =12.69

degree of freedom =5-1=4

hence p value =0.0129

2)for p value is less then 0.05 level data provide evidence that the grade distribution differs from theoritical projection.

3)for p value is greater then 0.01 level data does not provide sufficient evidence that the grade distribution differs from theoritical projection.

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E A 0.10 60.00 50.00 2.00 B 0.30 174.00 150.00 3.84 C 0.40 180.00 200.00 2.00 D 0.16 62.00 80.00 4.05 F 0.04 24.00 20.00 0.80 500 500 12.6900

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