**Coefficient of Association between Success in Examination and Residence in Hostel**

To find the coefficient of association between success in an examination and residence in the hostel, we need to calculate the contingency table and then use the formula for the coefficient of association.

Let's start by creating a contingency table based on the given data:

| | Residing in Hostel | Not Residing in Hostel |
|---------------------|--------------------|------------------------|
| Passed Examination | ? | ? |
| Failed Examination | ? | ? |

From the given information, we know that there are a total of 500 students in the college, out of which 200 students were residing in the hostel. We also know that 80% of the students passed the examination.

Now, let's calculate the missing values in the contingency table:

1. Number of students who passed the examination and were residing in the hostel:
- Total students = 500
- Passed examination = 80% of 500 = 400
- Not residing in hostel = 500 - 200 = 300
- Students who passed examination and were residing in the hostel = 400 - (300 x 0.4) = 280

2. Number of students who failed the examination and were residing in the hostel:
- Total students = 500
- Failed examination = 20% of 500 = 100
- Not residing in hostel = 500 - 200 = 300
- Students who failed examination and were residing in the hostel = 100 - (300 x 0.4) = -20

3. Number of students who passed the examination and were not residing in the hostel:
- Total students = 500
- Passed examination = 80% of 500 = 400
- Residing in hostel = 200
- Students who passed examination and were not residing in the hostel = 400 - 200 = 200

4. Number of students who failed the examination and were not residing in the hostel:
- Total students = 500
- Failed examination = 20% of 500 = 100
- Residing in hostel = 200
- Students who failed examination and were not residing in the hostel = 100 - 200 = -100

Now we have the complete contingency table:

| | Residing in Hostel | Not Residing in Hostel |
|---------------------|--------------------|------------------------|
| Passed Examination | 280 | 200 |
| Failed Examination | -20 | -100 |

The formula for the coefficient of association is:

Coefficient of Association = (ad - bc) / √(a+b)(c+d)(a+c)(b+d)

Here, a = 280, b = 200, c = -20, and d = -100.

Now, let's plug in these values into the formula:

Coefficient of Association = (280 x -100 - 200 x -20) / √((280+200)(-20-100)(280-20)(200-100))

Simplifying this equation will give us the coefficient of association between success in an examination and residence in the hostel.

Note: The negative values in the contingency table indicate that there might be some discrepancy or error in the given data, as we cannot have negative values for the