Question

A Dean wants to know whether grade distribution in a stats class is different based on modality (face-to-face vs. online). He knows that in face-to-face sections of the course, 20% get A's, 30% get B's, 25% get C's, 10% get D's, and 15% get F's. The results from online sections (100 Students) from the previous semester are detailed in the table below, along with the appropriate chi-square statistic. Since the Chi-square statistic is (.833) is less than the critical value, is there enough evidence to suggest that online grade distributions for the course are different?

               Expected        Observed       (0-E)² / E

A                 20                   19                  0.050

B                 30                   28                  0.133

C                 25                   24                  0.040

D               10                    11                  0.100

F                 15                   18                  0.600

Total             100                 100               0.833

Answer 1

Solution:

For the given Chi-square test for goodness-of-fit we are given

Test statistic = 0.833

Number of categories = k = 5

Degrees of freedom = k - 1 = 4

We assume α = 0.05

So, critical value by using Chi-square table or excel is given as below:

Critical value = 9.487729

Test statistic < Critical value

So, we do not reject the null hypothesis.

So, there is not enough evidence to suggest that online grade distributions for the course are different.