Question
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.
Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport
Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport
Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport
Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport
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GPT-4o mini
To analyze the survey of students, let's first summarize the data we have:
1. Total students surveyed: 80
2. Students who play in the band and play a sport: 24
3. Students who are not in the band and do not play a sport: 22
4. Total students in the band: 48
We can deduce the following:
- If there are 22 students who are not in the band and do not play a sport, that leaves us with \(80 - 22 = 58\) students who either play in the band or play a sport (or both).
- Out of the 58 students, we know 24 play in both the band and a sport, which means there are \(58 - 24 = 34\) students who either play in the band only or play sports only.
- Since there are 48 students in the band, and 24 of them play sports, this means \(48 - 24 = 24\) students are in the band but do not play a sport.
- This illustrates that the breakdown could be:
- Students in the Band only: 24
- Students in the Band and playing Sport: 24
- Students not in the Band but play a Sport: 10 (since \(34 - 24 = 10\))
Now, let's consider the arrangement for the rows and columns in a contingency table.
A reasonable setup is:
- **Columns** that could represent whether students are in the band or not:
- In a Band
- Not in a Band
- **Rows** that could represent whether students play a sport or not:
- Play a Sport
- Do Not Play a Sport
Thus, the best choice among the options to represent the categories would be:
**Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport**
The configuration allows us to clearly show the overlap between students in the band and those who play sports.
1. Total students surveyed: 80
2. Students who play in the band and play a sport: 24
3. Students who are not in the band and do not play a sport: 22
4. Total students in the band: 48
We can deduce the following:
- If there are 22 students who are not in the band and do not play a sport, that leaves us with \(80 - 22 = 58\) students who either play in the band or play a sport (or both).
- Out of the 58 students, we know 24 play in both the band and a sport, which means there are \(58 - 24 = 34\) students who either play in the band only or play sports only.
- Since there are 48 students in the band, and 24 of them play sports, this means \(48 - 24 = 24\) students are in the band but do not play a sport.
- This illustrates that the breakdown could be:
- Students in the Band only: 24
- Students in the Band and playing Sport: 24
- Students not in the Band but play a Sport: 10 (since \(34 - 24 = 10\))
Now, let's consider the arrangement for the rows and columns in a contingency table.
A reasonable setup is:
- **Columns** that could represent whether students are in the band or not:
- In a Band
- Not in a Band
- **Rows** that could represent whether students play a sport or not:
- Play a Sport
- Do Not Play a Sport
Thus, the best choice among the options to represent the categories would be:
**Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport**
The configuration allows us to clearly show the overlap between students in the band and those who play sports.
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