Suppose we know that at a University XYZ that 15% of students receive an A in their introductory statistics class, 20% receive a B, 30% receive a C, 10% receive a D, and the rest receive an F. For comparison, a sample of 250 students at University ABC is taken and 20% received an A, 25% received a B, 25% received a C, 10% received a D, and the remaining students failed the class. When testing (at the 5% level of significance) whether the proportions between the two universities are different, what is the critical value? (please round your answer to 3 decimal places)
Given Information:
University XYZ:
15% received A, 20% received B, 30% received C, 10% received D and the rest have failed.
Suppose university XYZ has 100 students in total. Then,
The number of students who received A is
The number of students who received B is
Similarly, the number of students who received C is 30.
The number of students who received D is 10.
The number of students who failed is .
University ABC:
20% received A, 25% received B, 25% received C, 10% received D and the remaining failed.
The sample size is 250.
So, the number of students who received A is
The number of students who received B is
The number of students who received C is .
The number of students who received D is .
The number of students who failed is .
The contingency table with observed frequencies is given below:
| University/Grade | A | B | C | D | F | Total |
| XYZ | 15 | 20 | 30 | 10 | 25 | 100 |
| ABC | 50 | 62.5 | 62.5 | 25 | 50 | 250 |
| Total | 65 | 82.5 | 92.5 | 35 | 75 | 350 |
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