[tex](05.05 \, MC)[/tex]

Male and female students were asked which location they would most want to visit. They had the following preferences:

[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
& Hawaii & Paris & Row Totals \\
\hline
Male students & 0.38 & 0.12 & 0.50 \\
\hline
Female students & 0.26 & 0.24 & 0.50 \\
\hline
Column totals & 0.64 & 0.36 & 1 \\
\hline
\end{tabular}
\][/tex]

Which of the following is a two-way conditional relative frequency table for gender? (1 point)

[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]

Which location would you most like to visit?
- Hawaii
- Paris
- Row totals



Answer :

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]