To create a conditional relative frequency table by column, we need to determine the proportion of students within each column category (Looking for Job and Not Looking for Job) relative to the total number of students in that column. Each relative frequency is calculated by dividing the frequency of a specific cell by the total frequency of its column.
Let's break this down step-by-step:
1. Total Students:
- Total = 150
2. Frequencies:
- Currently Employed and Looking for Job = 12
- Currently Employed and Not Looking for Job = 28
- Not Currently Employed and Looking for Job = 38
- Not Currently Employed and Not Looking for Job = 72
3. Column Totals:
- Total Looking for Job = 50
- Total Not Looking for Job = 100
4. Calculate the conditional relative frequencies by column:
- Currently Employed (Looking for Job):
[tex]\[
\text{Relative Frequency} = \frac{\text{Currently Employed and Looking for Job}}{\text{Total Looking for Job}} = \frac{12}{50} = 0.24
\][/tex]
- Currently Employed (Not Looking for Job):
[tex]\[
\text{Relative Frequency} = \frac{\text{Currently Employed and Not Looking for Job}}{\text{Total Not Looking for Job}} = \frac{28}{100} = 0.28
\][/tex]
- Not Currently Employed (Looking for Job):
[tex]\[
\text{Relative Frequency} = \frac{\text{Not Currently Employed and Looking for Job}}{\text{Total Looking for Job}} = \frac{38}{50} = 0.76
\][/tex]
- Not Currently Employed (Not Looking for Job):
[tex]\[
\text{Relative Frequency} = \frac{\text{Not Currently Employed and Not Looking for Job}}{\text{Total Not Looking for Job}} = \frac{72}{100} = 0.72
\][/tex]
Now, putting these conditional relative frequencies into a table format, we get:
[tex]\[
\begin{tabular}{|r|c|c|}
\cline{2-3}
\multicolumn{1}{c|}{} & \text{Looking for Job} & \begin{tabular}{c} \text{Not Looking for} \\\text{Job} \end{tabular}\\
\hline
\text{Currently Employed} & 0.24 & 0.28 \\
\hline
\text{Not Currently Employed} & 0.76 & 0.72 \\
\hline
\end{tabular}
\][/tex]
Thus, the conditional relative frequency table by column is:
[tex]\[
\begin{tabular}{|r|c|c|}
\cline{2-3}
\multicolumn{1}{c|}{} & \text{Looking for Job} & \begin{tabular}{c} \text{Not Looking for} \\\text{Job} \end{tabular}\\
\hline
\text{Currently Employed} & 0.24 & 0.28 \\
\hline
\text{Not Currently Employed} & 0.76 & 0.72 \\
\hline
\end{tabular}
\][/tex]
