Question

student spending survey
a high school economics teacher wants to understand the spending habits of students. the teacher surveys students about their preferred spending category (entertainment vs. education) and whether they save money regularly (yes vs. no).
the survey results are as follows:

• 200 students were surveyed in total.
• 80 students prefer spending on entertainment. of those, 50 save money regularly.
• 90 students save money regularly and prefer spending on education.
• the total number of students who do not save money regularly is 60.

the teacher plans to use this data to encourage better financial habits among students.

spending category	save money regularly (yes)	do not save regularly (no)	total
education	90

given that 30 students spend money on entertainment and do not save money regularly, what is the conditional relative frequency of students that prefer spending on entertainment and do not save money regularly?
options: 50%, 40%, 100%, 30%

Explanation:

Step1: Understand Conditional Relative Frequency

Conditional relative frequency is calculated as the number of favorable cases (students who prefer entertainment and do not save) divided by the number of cases in the given condition (students who spend on entertainment and do not save, which is 30 here). Wait, no—wait, the given condition is "30 students spend money on entertainment and do not save money regularly". We need the conditional relative frequency of students that prefer spending on entertainment and do not save money regularly, given that they are in the group of students who spend on entertainment and do not save. Wait, actually, the "given" group is the 30 students who spend on entertainment and do not save. So within that group, how many prefer entertainment and do not save? All 30, because the group is defined as those who spend on entertainment and do not save. So the number of favorable is 30, the total in the condition is 30. So \( \frac{30}{30} = 1 = 100\% \).

Step2: Calculate the Ratio

Using the formula for conditional relative frequency: \( \text{Conditional Relative Frequency} = \frac{\text{Number of students in both categories (entertainment and not save)}}{\text{Number of students in the given category (entertainment and not save)}} \). Plugging in the numbers: \( \frac{30}{30} = 1 \), which is 100%.

Answer:

100%