To find the conditional relative frequency table by columns, we need to calculate the relative frequencies based on the total number of students in each column.
Let's break down the process step-by-step for clarity.
Step 1: Calculate the Conditional Relative Frequencies for "Currently Employed"
- Looking for Job:
[tex]\[
\text{Currently Employed Looking for Job} = \frac{\text{Number of Employed Looking for Job}}{\text{Total Looking for Job}} = \frac{12}{50} = 0.24
\][/tex]
- Not Looking for Job:
[tex]\[
\text{Currently Employed Not Looking for Job} = \frac{\text{Number of Employed Not Looking for Job}}{\text{Total Not Looking for Job}} = \frac{28}{100} = 0.28
\][/tex]
Step 2: Calculate the Conditional Relative Frequencies for "Not Currently Employed"
- Looking for Job:
[tex]\[
\text{Not Currently Employed Looking for Job} = \frac{\text{Number of Not Employed Looking for Job}}{\text{Total Looking for Job}} = \frac{38}{50} = 0.76
\][/tex]
- Not Looking for Job:
[tex]\[
\text{Not Currently Employed Not Looking for Job} = \frac{\text{Number of Not Employed Not Looking for Job}}{\text{Total Not Looking for Job}} = \frac{72}{100} = 0.72
\][/tex]
Step 3: Calculate the Overall Conditional Relative Frequencies for Employment Status
- Currently Employed Total:
[tex]\[
\text{Total Currently Employed} = \frac{\text{Total Employed}}{\text{Total Students}} = \frac{40}{150} \approx 0.267
\][/tex]
- Not Currently Employed Total:
[tex]\[
\text{Total Not Currently Employed} = \frac{\text{Total Not Employed}}{\text{Total Students}} = \frac{110}{150} \approx 0.733
\][/tex]
Therefore, the conditional relative frequency table by column is:
Job Status
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{} & \text{Looking for Job} & \text{Not Looking for Job} & \text{Total} \\
\hline
\text{Currently Employed} & 0.24 & 0.28 & 0.267 \\
\hline
\text{Not Currently Employed} & 0.76 & 0.72 & 0.733 \\
\hline
\end{array}
\][/tex]
