Let's solve this step-by-step using the information given in the table and calculating the appropriate two-way conditional relative frequencies for male and female students.
1. Identify Initial Data:
- Male students preferring Hawaii: 0.38
- Male students preferring Paris: 0.12
- Total male students: 0.50
- Female students preferring Hawaii: 0.26
- Female students preferring Paris: 0.24
- Total female students: 0.50
2. Calculate Conditional Relative Frequencies for Male Students:
- Proportion of male students who prefer Hawaii:
[tex]\[
\frac{0.38}{0.50} = 0.76
\][/tex]
- Proportion of male students who prefer Paris:
[tex]\[
\frac{0.12}{0.50} = 0.24
\][/tex]
3. Calculate Conditional Relative Frequencies for Female Students:
- Proportion of female students who prefer Hawaii:
[tex]\[
\frac{0.26}{0.50} = 0.52
\][/tex]
- Proportion of female students who prefer Paris:
[tex]\[
\frac{0.24}{0.50} = 0.48
\][/tex]
4. Construct the Two-Way Conditional Relative Frequency Table:
The two-way conditional relative frequency table for gender, based on the calculations, is:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Hawaii & Paris & Row totals \\
\hline Male students & 0.76 & 0.24 & 1 \\
\hline Female students & 0.52 & 0.48 & 1 \\
\hline
\end{tabular}
\][/tex]
So, the two-way conditional relative frequency table for gender is:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Hawaii & Paris & Row totals \\
\hline Male students & 0.76 & 0.24 & 1 \\
\hline Female students & 0.52 & 0.48 & 1 \\
\hline
\end{tabular}
\][/tex]
