A table represents the number of students who passed or failed an aptitude test at two different campuses.

**East Campus**

**West Campus**

**Passed**

39

45

**Failed**

61

55


In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed.


**What is the expected frequency of East Campus and passed?**

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.

A table represents the number of students who passed or failed an aptitude test at two different campuses. East Campus Passed: 39, East Campus Failed: 61, West Campus Passed: 45, West Campus Failed: 55. In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of East Campus and passed?

Learn how to calculate the expected frequency for 'East Campus and Passed' in a contingency table using the chi-square test for independence. This statistical method helps determine if there's a significant difference in pass rates between campuses. Suitable for high school seniors or college students.

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