To determine the expected frequency for the "East Campus and Passed" category using the Chi-square test for independence, we follow these steps:

Step 1: Calculate Row Totals

• Passed Total: $39 + 45 = 84$
• Failed Total: $61 + 55 = 116$

Step 2: Calculate Column Totals

• East Campus Total: $39 + 61 = 100$
• West Campus Total: $45 + 55 = 100$

Step 3: Calculate the Grand Total

• Grand Total: $100 + 100 = 200$

Step 4: Calculate Expected Frequency

The formula for the expected frequency in a contingency table is:

$E = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}$

For the "East Campus and Passed" category:

$E = \frac{(84) \times (100)}{200} = \frac{8400}{200} = 42$

The expected frequency for East Campus and Passed is 42.

Do you want further details or explanations on the steps? Here are some related questions:

1. What is the expected frequency for West Campus and Passed?
2. What is the chi-square statistic formula and how is it applied in this case?
3. How do we determine the degrees of freedom in a chi-square test?
4. What is the significance level for a chi-square test, and how is it chosen?
5. How can we interpret the result of a chi-square test?

Tip: The expected frequencies must be calculated for each cell before performing the chi-square test, ensuring you have all the necessary values.