- The data is categorical, making the first statement false.
- The percentage of boys without pets (\(\approx 53.3\%\)) is greater than that of girls (\(35\%\)), making the second statement false.
- The total number of girls with 2 or more pets is \(7\) (\(5+2\)), not \(2\), making the third statement false.
- More girls own at least one pet (\(13\)) than no pets (\(7\)), making the fourth statement false.
- None of the statements provided are true based on the data. \(\boxed{\text{None of the statements are true.}}\)
Explanation
- Analyze the Data and Statement 1
To determine which statement is true, we first examine the data provided in the two-way frequency table:
- Total number of Boys: \(8 + 4 + 3 + 0 = 15\)
- Total number of Girls: \(7 + 6 + 5 + 2 = 20\)
- Categorization: The survey collects data on gender and categories of pets, which is categorical data, not purely quantitative numerical data. This means the first statement is false.
- Analyze Statement 2
We calculate the percentage of boys and girls who do not own a pet:
- Percentage of boys with 0 pets: \(\frac{8}{15} \approx 53.3\%\).
- Percentage of girls with 0 pets: \(\frac{7}{20} = 35\%\).
Comparing these values, the percentage of girls who do not own a pet (\(35\%\)) is not greater than the percentage of boys who do not own a pet (\(53.3\%\)). Thus, the second statement is false.
- Analyze Statement 3
We calculate the total number of girls who own 2 or more pets by adding the counts in the "2 pets" column and the "More than 2 pets" column:
- Girls with 2 or more pets: \(5 + 2 = 7\).
The statement says the total is \(2\), which is incorrect because the count for those with 2 pets alone is \(5\), and the count for those with more than 2 pets is \(2\). Thus, the third statement is false.
- Analyze Statement 4 and Conclude
We compare the number of girls who do not own a pet to those who do:
- Girls with 0 pets: \(7\).
- Girls who own at least one pet: \(6 + 5 + 2 = 13\).
Since \(7 < 13\), there are fewer girls who do not own a pet compared to those who do. Therefore, the fourth statement is false.
Upon careful review, none of the provided statements are true according to the data in the table. However, if forced to identify the most accurate evaluation, we conclude that based on the provided data, all four listed options are mathematically false. In a real-world assessment context, please verify the problem's text again. Assuming no errors in the question transcription, there is no correct statement among the choices. If this were a multiple-choice question with a typo in the options, one might need to reconsider the intended logic. Given the options provided and the data in the table, the correct response is that none of the statements is true.
Examples
In real-world data analysis, two-way frequency tables are used to compare categorical data, such as comparing pet ownership across different demographic groups. For example, a local animal shelter could use this type of analysis to determine which neighborhoods might be more interested in adopting certain types of animals, helping them plan outreach programs effectively by understanding their target audience composition.