Let's analyze the two-way table and calculate the relative frequencies for the specified groups.
Given:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{1}{|c|}{} & Alaska & \begin{tabular}{c}
Not \\
Alaska
\end{tabular} & Total \\
\hline Hawaii & 6 & 15 & 21 \\
\hline \begin{tabular}{c}
Not \\
Hawaii
\end{tabular} & 8 & 21 & 29 \\
\hline Total & 14 & 36 & 50 \\
\hline
\end{tabular}
\][/tex]
Total number of students, [tex]\( N = 50 \)[/tex].
### 1. Relative frequency for students who have been to Alaska
From the table, the total number of students who have been to Alaska is 14.
The relative frequency is calculated as:
[tex]\[
\text{Relative frequency for Alaska} = \frac{\text{Number of students who have been to Alaska}}{\text{Total number of students}} = \frac{14}{50} = 0.28
\][/tex]
### 2. Relative frequency for students who have been to Hawaii but not Alaska
From the table, the number of students who have been to Hawaii but not Alaska is 15.
The relative frequency is calculated as:
[tex]\[
\text{Relative frequency for Hawaii but not Alaska} = \frac{\text{Number of students who have been to Hawaii but not Alaska}}{\text{Total number of students}} = \frac{15}{50} = 0.3
\][/tex]
### 3. Relative frequency for students who have not been to Alaska or Hawaii
From the table, the number of students who have not been to Alaska or Hawaii is 21.
The relative frequency is calculated as:
[tex]\[
\text{Relative frequency for not Alaska and not Hawaii} = \frac{\text{Number of students who have not been to Alaska or Hawaii}}{\text{Total number of students}} = \frac{21}{50} = 0.42
\][/tex]
### Summary of Relative Frequencies
- The relative frequency for students who have been to Alaska is [tex]\(0.28\)[/tex].
- The relative frequency for students who have been to Hawaii but not Alaska is [tex]\(0.3\)[/tex].
- The relative frequency for students who have not been to Alaska or Hawaii is [tex]\(0.42\)[/tex].
