The two-way frequency table represents data from a survey asking a random sampling of people whether they can see the sunrise or sunset from the front of their home.

\begin{tabular}{|c|c|c|c|}
\hline & Sunrise & No Sunrise & Total \\
\hline Sunset & 14 & 12 & 26 \\
\hline No Sunset & 7 & 5 & 12 \\
\hline Total & 21 & 17 & 38 \\
\hline
\end{tabular}

Which is the joint relative frequency for the people who can only see the sunset?
A. [tex]$\frac{5}{38}$[/tex]
B. [tex]$\frac{7}{2 n}$[/tex]



Answer :

To determine the joint relative frequency for the people who can only see the sunset, we need to follow these steps:

1. Understand the Table:
- The table categorizes data based on whether people can see the sunrise and/or the sunset.
- The rows and columns provide counts for people who can see the sunset and sunrise, respectively, and those who cannot.

2. Identify the Relevant Count:
- We are asked for the joint relative frequency of people who can only see the sunset.
- In the table, the count for people who can only see the sunset is found in the "Sunset" row under the "No Sunrise" column.
- This value is 7.

3. Calculate the Joint Relative Frequency:
- The joint relative frequency is calculated by dividing the count of people who can only see the sunset by the total number of respondents.
- From the table, the total number of respondents is 38.

Hence, the joint relative frequency is:
[tex]\[ \frac{\text{Number of people who can only see the sunset}}{\text{Total number of people surveyed}} = \frac{7}{38} \][/tex]

4. Convert to Decimal (Optional):
- In this particular problem, we provide the relative frequency as a fraction, which is:
[tex]\[ \frac{7}{38} \][/tex]

Thus, the joint relative frequency for the people who can only see the sunset is [tex]\(\frac{7}{38}\)[/tex].

When evaluated numerically, this fraction equals approximately [tex]\(0.18421052631578946\)[/tex], but [tex]\(\frac{7}{38}\)[/tex] is the exact joint relative frequency for the people who can only see the sunset.