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

\begin{tabular}{|c|c|c|}
\hline & East Campus & West Campus \\
\hline Passed & 48 & 37 \\
\hline Failed & 52 & 63 \\
\hline
\end{tabular}

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

What is the expected frequency of students who failed at the West Campus?

Sagot :

To determine the expected frequency of students who failed at the West Campus, we follow these steps:

1. Gather the Observed Frequencies:
- Passed at East Campus: 48
- Passed at West Campus: 37
- Failed at East Campus: 52
- Failed at West Campus: 63

2. Calculate the Total Number of Students at Each Campus:
- Total students at East Campus [tex]\( = 48 + 52 = 100 \)[/tex]
- Total students at West Campus [tex]\( = 37 + 63 = 100 \)[/tex]

3. Calculate the Total Number of Students Who Passed or Failed:
- Total students who passed [tex]\( = 48 + 37 = 85 \)[/tex]
- Total students who failed [tex]\( = 52 + 63 = 115 \)[/tex]

4. Calculate the Total Number of Students Overall:
- Total students overall [tex]\( = 100 + 100 = 200 \)[/tex]

5. Use the Formula for Expected Frequency:
The expected frequency for a cell in a contingency table can be calculated using the formula:
[tex]\[ \text{Expected Frequency} = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}} \][/tex]
Here, we need the expected frequency of students who failed at the West Campus.
- Row Total (Total Failures): [tex]\( 115 \)[/tex]
- Column Total (Total students at West Campus): [tex]\( 100 \)[/tex]
- Grand Total (Total Students Overall): [tex]\( 200 \)[/tex]

Plugging in these values:
[tex]\[ \text{Expected Frequency of Failed at West Campus} = \frac{(115 \times 100)}{200} = 57.5 \][/tex]

Therefore, the expected frequency of students who failed at the West Campus is 57.5.