Let's analyze the findings step by step and verify the statements concerning the two-way frequency table.
1. Percentage of Boys and Girls Who Do Not Own a Pet:
For boys:
- Total number of boys: 15
- Number of boys with 0 pets: 8
- Percentage of boys with 0 pets: [tex]\(\frac{8}{15} \times 100 \approx 53.33\%\)[/tex]
For girls:
- Total number of girls: 20
- Number of girls with 0 pets: 7
- Percentage of girls with 0 pets: [tex]\(\frac{7}{20} \times 100 = 35\%\)[/tex]
This indicates that a larger percentage of boys do not own pets compared to girls.
2. Total Number of Girls Who Own 2 or More Pets:
- Number of girls with exactly 2 pets: 5
- Number of girls with more than 2 pets: 2
- Total number of girls with 2 or more pets: [tex]\(5 + 2 = 7\)[/tex]
3. Majority of Girls Not Owning a Pet:
- Number of girls not owning a pet: 7
- Total number of girls: 20
- Since 7 out of 20 is 35%, which is less than 50%, less than half of the girls do not own a pet.
Given the detailed calculations and verifications, we can now examine each statement:
1. The survey represents quantitative data:
- The survey in question involves counting the number of pets, which is a categorical variable. Thus, this statement is false.
2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet:
- The percentage of boys not owning pets is approximately 53.33%, while the percentage for girls is 35%. Therefore, this statement is false.
3. The total number of girls who own 2 or more pets is 2:
- We calculated that the total number of girls with 2 or more pets is 7, which makes this statement false.
4. More girls do not own a pet than do own a pet:
- With only 7 out of 20 girls not owning a pet, this number does not exceed the 13 girls who own at least one pet. Therefore, this statement is false.
To conclude, none of the given statements about the two-way frequency table are true.
