In: Statistics and Probability
4. Assume that the Graduation Rate is classified into 3 categories (Low, Medium, High) in the following way:
Low is considered to be a rate that is less than 0.66,
Medium is between 0.66 and less than 0.80, and
High is at least 0.80.
Assume that the Student-to-Faculty ratio is also classified into 3 categories:
Category 1: Up to 10 student-to-faculty ratio,
Category 2: between 11 and 18 student-to-faculty ratio
Category 3: greater than 18 student-to-faculty ratio
The following contingency table summarizes the categorized information :
Graduation Rate |
Student-to-Faculty Ratio |
|||
Category1 (≤10) |
Category2 (between 11 and 18) |
Category3 ( > 18) |
Σ |
|
Low (< 0.66) |
9 |
77 |
27 |
113 |
Medium (≥0.66 and < 0.80) |
21 |
20 |
2 |
43 |
High (≥0.80) |
26 |
10 |
0 |
36 |
Σ |
56 |
107 |
29 |
192 |
Using these defined categories, determine if the student-to-faculty ratio is independent of the graduation rate. Test this at a 0.05 level of significance.
What is your conclusion?