Answer :
Let's examine the statements one by one, based on the data and results provided.
### 1. The survey represents quantitative data.
This statement is false. The survey collects categorical data about the number of pets in students' households. The number of pets is a discrete, countable quantity, which is considered categorical rather than quantitative.
### 2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
To determine this, we need to calculate the percentages of boys and girls who do not own a pet.
- Boys who do not own a pet:
- Number of boys who do not own a pet = 8
- Total number of boys = 15
- Percentage of boys who do not own a pet = [tex]\(\frac{8}{15} \times 100 \approx 53.33\%\)[/tex]
- Girls who do not own a pet:
- Number of girls who do not own a pet = 7
- Total number of girls = 20
- Percentage of girls who do not own a pet = [tex]\(\frac{7}{20} \times 100 = 35.0\%\)[/tex]
Comparing these percentages:
- Percentage of boys who do not own a pet = 53.33%
- Percentage of girls who do not own a pet = 35.0%
Since 53.33% (boys) is greater than 35.0% (girls), there is not a greater percentage of girls who do not own a pet compared to boys. Therefore, this statement is false.
### 3. The total number of girls who own 2 or more pets is 2.
Let's calculate the number of girls who own 2 or more pets:
- Girls with exactly 2 pets = 5
- Girls with more than 2 pets = 2
- Total number of girls who own 2 or more pets = 5 + 2 = 7
The statement that the total number of girls who own 2 or more pets is 2 is false.
### 4. More girls do not own a pet than do own a pet.
To verify this, let's compare the number of girls who do not own a pet with the number who do:
- Number of girls who do not own a pet = 7
- Number of girls who own at least one pet = 20 - 7 = 13
Since 7 is less than 13, more girls own at least one pet than do not own any. Therefore, this statement is false.
### Conclusion
Based on the data analysis, none of the proposed statements about the two-way frequency table is true.
### 1. The survey represents quantitative data.
This statement is false. The survey collects categorical data about the number of pets in students' households. The number of pets is a discrete, countable quantity, which is considered categorical rather than quantitative.
### 2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
To determine this, we need to calculate the percentages of boys and girls who do not own a pet.
- Boys who do not own a pet:
- Number of boys who do not own a pet = 8
- Total number of boys = 15
- Percentage of boys who do not own a pet = [tex]\(\frac{8}{15} \times 100 \approx 53.33\%\)[/tex]
- Girls who do not own a pet:
- Number of girls who do not own a pet = 7
- Total number of girls = 20
- Percentage of girls who do not own a pet = [tex]\(\frac{7}{20} \times 100 = 35.0\%\)[/tex]
Comparing these percentages:
- Percentage of boys who do not own a pet = 53.33%
- Percentage of girls who do not own a pet = 35.0%
Since 53.33% (boys) is greater than 35.0% (girls), there is not a greater percentage of girls who do not own a pet compared to boys. Therefore, this statement is false.
### 3. The total number of girls who own 2 or more pets is 2.
Let's calculate the number of girls who own 2 or more pets:
- Girls with exactly 2 pets = 5
- Girls with more than 2 pets = 2
- Total number of girls who own 2 or more pets = 5 + 2 = 7
The statement that the total number of girls who own 2 or more pets is 2 is false.
### 4. More girls do not own a pet than do own a pet.
To verify this, let's compare the number of girls who do not own a pet with the number who do:
- Number of girls who do not own a pet = 7
- Number of girls who own at least one pet = 20 - 7 = 13
Since 7 is less than 13, more girls own at least one pet than do not own any. Therefore, this statement is false.
### Conclusion
Based on the data analysis, none of the proposed statements about the two-way frequency table is true.
