Question

determining relative frequency ratios
the following two - way table represents data from a survey asking students whether they have visited alaska, hawaii, or both.

	alaska	not alaska	total
not hawaii	8	21	29
total	14	36	50

what is the relative frequency for students who have been to alaska?
dropdown
what is the relative frequency for students who have been to hawaii but not alaska?
dropdown
what is the relative frequency for students who have not been to alaska or hawaii?
dropdown
options (for the last dropdown, shown partially): 6/50, 6/21, 21/50, 21/36

Explanation:

Sub - Question 1: Relative Frequency for Students Who Have Been to Alaska

Step 1: Find Total Number of Students

The total number of students is the sum of all the values in the "Total" row (or column). From the table, the total number of students is \(50\) (since \(21 + 29=50\) or \(14 + 36 = 50\)).

Step 2: Find Number of Students Who Have Been to Alaska

The number of students who have been to Alaska is the sum of the values in the "Alaska" column. So, \(6+8 = 14\).

Step 3: Calculate Relative Frequency

Relative frequency is calculated as the number of favorable outcomes (students who have been to Alaska) divided by the total number of outcomes (total number of students). So, the relative frequency is \(\frac{14}{50}=\frac{7}{25} = 0.28\) (or \(\frac{14}{50}\) can be simplified, but also note that from the table, the "Total" for Alaska is \(14\) and total students is \(50\), so relative frequency is \(\frac{14}{50}=\frac{7}{25}\) or \(0.28\)). But looking at the options, we can also note that the number of students who have been to Alaska is \(14\) and total is \(50\), so \(\frac{14}{50}=\frac{7}{25}\) (or in the form of the options, if we consider the counts, the relative frequency is \(\frac{14}{50}=\frac{7}{25}\), but also, from the table, the "Alaska" total is \(14\), so relative frequency is \(\frac{14}{50}\)).

Step 1: Identify the Number of Students Who Have Been to Hawaii but Not Alaska

From the table, in the "Hawaii" row and "Not Alaska" column, the number of students is \(15\).

Step 2: Use Total Number of Students

The total number of students is \(50\) (as calculated before).

Step 3: Calculate Relative Frequency

Relative frequency is the number of students who have been to Hawaii but not Alaska divided by the total number of students. So, the relative frequency is \(\frac{15}{50}=\frac{3}{10}=0.3\).

Step 1: Identify the Number of Students Who Have Not Been to Alaska or Hawaii

From the table, in the "Not Hawaii" row and "Not Alaska" column, the number of students is \(21\).

Step 2: Use Total Number of Students

The total number of students is \(50\).

Step 3: Calculate Relative Frequency

Relative frequency is the number of students who have not been to Alaska or Hawaii divided by the total number of students. So, the relative frequency is \(\frac{21}{50}=0.42\) (or \(\frac{21}{50}\)).

Answer:

\(\frac{14}{50}\) (or \(\frac{7}{25}\) or \(0.28\))

Sub - Question 2: Relative Frequency for Students Who Have Been to Hawaii but Not Alaska