Question

	sunrise	no sunrise	total
sunset	14	12	26
no sunset	7	5	12
total	21	17	38

which is the joint relative frequency for the people who can only see the sunset?
\\(\frac{5}{38}\\)
\\(\frac{7}{38}\\)
\\(\frac{12}{38}\\)
\\(\frac{14}{38}\\)

Explanation:

Step1: Understand Joint Relative Frequency

Joint relative frequency is calculated as the frequency of a specific category divided by the total number of observations.

Step2: Identify the Relevant Cell and Total

For people who can only see the sunset, we look at the cell where "Sunset" and "No Sunrise" intersect, which has a frequency of 12? Wait, no, wait. Wait, "only see the sunset" means they see sunset but no sunrise. Wait, the table: Sunset row, No Sunrise column is 12? Wait, no, wait the options: Wait, the total number of people is 38 (from the Total row, Total column). Wait, let's re-examine the table.

Wait, the table:

• Sunset row: Sunrise (14), No Sunrise (12), Total (26)
• No Sunset row: Sunrise (7), No Sunrise (5), Total (12)
• Total row: Sunrise (21), No Sunrise (17), Total (38)

"Only see the sunset" means they see sunset (so in Sunset row) and do not see sunrise (No Sunrise column). So the frequency is 12? Wait, but the options have 12/38? Wait, no, wait the options:

Wait the options are 5/38, 7/38, 12/38, 14/38.

Wait, maybe I misinterpret "only see the sunset". Wait, maybe "only see the sunset" means they see sunset and do not see sunrise? Wait, but the cell for Sunset and No Sunrise is 12. Then the joint relative frequency is 12 (frequency of Sunset and No Sunrise) divided by total (38). So 12/38. Wait, but let's check:

Joint relative frequency for a cell is (cell value) / (grand total). The grand total is 38.

So "people who can only see the sunset" – that would be Sunset (yes) and Sunrise (no), so the cell is Sunset row, No Sunrise column, which is 12. So 12/38. So the answer is 12/38.

Wait, but let's confirm:

Joint relative frequency = (frequency of the category) / (total number of observations)

Total number of observations is 38 (from the Total row, Total column).

The category "only see the sunset" – so they see sunset (Sunset row) and do not see sunrise (No Sunrise column). The frequency for that cell is 12. So 12/38.

So the correct option is 12/38.

Answer:

$\frac{12}{38}$ (corresponding to the option with $\frac{12}{38}$)