Let's analyze the table and statements in detail to determine which is true.
Given:
- Boys with 0 pets: 8
- Girls with 0 pets: 7
- Total boys: 15
- Total girls: 20
First, let's calculate the relevant percentages and other values mentioned in the statements:
1. Percentage of boys who do not own a pet:
[tex]\[
\frac{\text{Boys with 0 pets}}{\text{Total boys}} \times 100 = \frac{8}{15} \times 100 \approx 53.33\%
\][/tex]
2. Percentage of girls who do not own a pet:
[tex]\[
\frac{\text{Girls with 0 pets}}{\text{Total girls}} \times 100 = \frac{7}{20} \times 100 = 35.00\%
\][/tex]
3. Total number of girls who own 2 or more pets:
- 2 pets: [tex]\(5\)[/tex]
- More than 2 pets: [tex]\(2\)[/tex]
[tex]\[
5 + 2 = 7
\][/tex]
4. Comparing the number of girls who own a pet versus those who do not:
- Girls who do not own a pet: [tex]\(7\)[/tex]
- Girls who own a pet: [tex]\(20 - 7 = 13\)[/tex]
Since [tex]\(13 > 7\)[/tex], more girls own a pet than do not own a pet.
Now let's evaluate the given statements:
- The survey represents quantitative data.: This is incorrect because the number of pets is categorical data, not quantitative.
- There is a greater percentage of girls who do not own a pet than boys who do not own a pet.: This is incorrect. The percentage of boys who do not own a pet ([tex]\(\approx 53.33\%\)[/tex]) is greater than the percentage of girls who do not own a pet ([tex]\(35.00\%\)[/tex]).
- The total number of girls who own 2 or more pets is 2.: This is incorrect. As calculated, the total number of girls who own 2 or more pets is [tex]\(7\)[/tex].
- More girls do not own a pet than do own a pet.: This is incorrect. There are more girls who own a pet ([tex]\(13\)[/tex]) than those who do not own a pet ([tex]\(7\)[/tex]).
None of the provided statements about the two-way frequency table is true based on the given calculations.
