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Determining Relative Frequency Ratios

The following two-way table represents data from a survey asking students whether they have visited Alaska, Hawaii, or both.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Alaska & \begin{tabular}{c}
Not \\
Alaska
\end{tabular} & Total \\
\hline Hawaii & 6 & 15 & 21 \\
\hline \begin{tabular}{c}
Not \\
Hawaii
\end{tabular} & 8 & 21 & 29 \\
\hline Total & 14 & 36 & 50 \\
\hline
\end{tabular}
\][/tex]

1. What is the relative frequency for students who have been to Alaska? [tex]$\square$[/tex]
2. What is the relative frequency for students who have been to Hawaii but not Alaska? [tex]$\square$[/tex]
3. What is the relative frequency for students who have not been to Alaska or Hawaii? [tex]$\square$[/tex]

Sagot :

GinnyAnswer
To determine the relative frequencies for the given survey data, we need to follow these steps:

### 1. Relative Frequency for Students Who Have Been to Alaska

- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have been to Alaska: [tex]\( 14 \)[/tex]

The relative frequency, [tex]\( f \)[/tex], for students who have been to Alaska is calculated as:
[tex]\[ f = \frac{\text{Number of students who have been to Alaska}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{14}{50} \][/tex]
[tex]\[ f = 0.28 \][/tex]

So, the relative frequency for students who have been to Alaska is [tex]\( \boxed{0.28} \)[/tex].

### 2. Relative Frequency for Students Who Have Been to Hawaii but Not Alaska

- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have been to Hawaii but not Alaska: [tex]\( 15 \)[/tex]

The relative frequency, [tex]\( f \)[/tex], for students who have been to Hawaii but not Alaska is calculated as:
[tex]\[ f = \frac{\text{Number of students who have been to Hawaii but not Alaska}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{15}{50} \][/tex]
[tex]\[ f = 0.3 \][/tex]

So, the relative frequency for students who have been to Hawaii but not Alaska is [tex]\( \boxed{0.3} \)[/tex].

### 3. Relative Frequency for Students Who Have Not Been to Alaska or Hawaii

- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have not been to Alaska or Hawaii: [tex]\( 21 \)[/tex]

The relative frequency, [tex]\( f \)[/tex], for students who have not been to Alaska or Hawaii is calculated as:
[tex]\[ f = \frac{\text{Number of students who have not been to Alaska or Hawaii}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{21}{50} \][/tex]
[tex]\[ f = 0.42 \][/tex]

So, the relative frequency for students who have not been to Alaska or Hawaii is [tex]\( \boxed{0.42} \)[/tex].

In summary:
- 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].
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