Question

Suppose we collect data on the preferred mode of transportation (car, bus, bike) and the preferred leisure activity (reading, watching movies, playing sports) among JAG high school students. The table below shows the relative row frequencies.

car bus bike
reading 30 15 10
watching movies 50 20 5
playing sports 25 10 35
Which of the following is a correct interpretation about the preferred mode of transportation and the preferred leisure activity at JAG high school based on the table?
Responses

A There appears to be no association between preferred mode of transportation and the preferred leisure activity.There appears to be no association between preferred mode of transportation and the preferred leisure activity.

B There appears to be no association between preferring playing sports and preferring biking.There appears to be no association between preferring playing sports and preferring biking.

C There appears to be an association between preferring cars for a mode of transporation and preferring to watch movies as a leisure time activity. There are approximately 30% of the students who prefer cars and like to watch movies during their leisure time.There appears to be an association between preferring cars for a mode of transporation and preferring to watch movies as a leisure time activity. There are approximately 30% of the students who prefer cars and like to watch movies during their leisure time.

D There appears to be an association between preferring playing sports and preferring biking. 17.5% of the students who like to play sports prefer bikes. It is a much higher percentage compared to those who prefer bikes with a different preferred leisure activities.

Answer 1

Let's analyze the data given in the table. The relative frequencies for preferred modes of transportation among different leisure activities are as follows:

- **Reading**:
- Car: 30
- Bus: 15
- Bike: 10

- **Watching Movies**:
- Car: 50
- Bus: 20
- Bike: 5

- **Playing Sports**:
- Car: 25
- Bus: 10
- Bike: 35

To understand the frequencies, it’s important to look at each category and how they relate.

1. **Preferred leisure activity and its associated mode of transportation**:
- For **reading**, the highest preferred mode is **car** (30%).
- For **watching movies**, it is also the **car** (50%).
- For **playing sports**, the most preferred is the **bike** (35%).

Now, let's evaluate the interpretations:

**A**: There appears to be no association between preferred mode of transportation and the preferred leisure activity.
- This statement is **incorrect** because we see varying preferences for transportation based on leisure activity.

**B**: There appears to be no association between preferring playing sports and preferring biking.
- This statement is **incorrect** because a significant percentage of students who prefer playing sports prefer biking (35%).

**C**: There appears to be an association between preferring cars for a mode of transportation and preferring to watch movies as a leisure time activity. There are approximately 30% of the students who prefer cars and like to watch movies during their leisure time.
- This statement is **partially incorrect** because approximately 50% of the students who prefer watching movies like cars, not 30%.

**D**: There appears to be an association between preferring playing sports and preferring biking. 17.5% of the students who like to play sports prefer bikes. It is a much higher percentage compared to those who prefer bikes with different preferred leisure activities.
- This statement is **incorrect** in stating the percentage as 17.5% — it should be 35%. However, the association part is correct.

Based on this analysis, none of the options are fully correct, but **D** contains the correct association but has an incorrect percentage value. Therefore, if forced to choose, option **D** might be the closest interpretation overall since it references the connection between preferring biking and playing sports. In its current form, it carries some truth despite the percentage error.