To create a two-way conditional relative frequency table for gender, we will focus on the relative frequencies of preferences for each gender. This involves examining the proportion of students within each gender who prefer each location.
Given the data:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline \text{Which location would you most like to visit?} \\
\hline & \text{Hawaii} & \text{Paris} & \text{Row totals} \\
\hline \text{Male students} & 0.38 & 0.12 & 0.50 \\
\hline \text{Female students} & 0.26 & 0.24 & 0.50 \\
\hline \text{Column totals} & 0.64 & 0.36 & 1 \\
\hline
\end{array}
\][/tex]
We need to summarize the frequencies in a two-way table that condenses these preferences based on gender.
### Step-by-Step Solution:
1. Identify the given probabilities:
- For male students:
- The proportion who prefer Hawaii: [tex]\( P(\text{Hawaii} \mid \text{Male}) = 0.38 \)[/tex]
- The proportion who prefer Paris: [tex]\( P(\text{Paris} \mid \text{Male}) = 0.12 \)[/tex]
- The total proportion of male students: [tex]\( P(\text{Male}) = 0.50 \)[/tex]
- For female students:
- The proportion who prefer Hawaii: [tex]\( P(\text{Hawaii} \mid \text{Female}) = 0.26 \)[/tex]
- The proportion who prefer Paris: [tex]\( P(\text{Paris} \mid \text{Female}) = 0.24 \)[/tex]
- The total proportion of female students: [tex]\( P(\text{Female}) = 0.50 \)[/tex]
2. Construct the two-way conditional relative frequency table:
For Male students:
- The number who would like to visit Hawaii is [tex]\( 0.38 \)[/tex]
- The number who would like to visit Paris is [tex]\( 0.12 \)[/tex]
- Total number (proportion) of Male students is [tex]\( 0.50 \)[/tex]
For Female students:
- The number who would like to visit Hawaii is [tex]\( 0.26 \)[/tex]
- The number who would like to visit Paris is [tex]\( 0.24 \)[/tex]
- Total number (proportion) of Female students is [tex]\( 0.50 \)[/tex]
3. Tabulate these proportions:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline & \text{Hawaii} & \text{Paris} & \text{Total} \\
\hline \text{Male} & 0.38 & 0.12 & 0.50 \\
\hline \text{Female} & 0.26 & 0.24 & 0.50 \\
\hline
\end{array}
\][/tex]
This table summarizes the two-way conditional relative frequencies for student preferences based on gender. The rows indicate the gender, while the columns represent the preference for each location and the totals.
