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Sagot :
Let's analyze the given table and determine the truthfulness of each statement based on the survey data:
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Own a Car} & \text{Do Not Own a Car} & \text{Total} \\ \hline \text{LA residents} & 3,251 & 869 & 4,120 \\ \hline \text{NYC residents} & 1,478 & 6,182 & 7,660 \\ \hline \text{Total} & 4,729 & 7,051 & 11,780 \\ \hline \end{array} \][/tex]
### Breakdown of the Statements:
1. The survey represents quantitative data.
A survey is classified into qualitative or quantitative data. In this case, we are categorizing residents by whether they own a car or not. These categories are qualitative and not quantitative as we are dealing with categories, not numerical measurements. Therefore, this statement is "False."
2. There is a greater percentage of LA residents who own a car than NYC residents who do.
- LA residents:
- Total residents surveyed: [tex]\( 3251 + 869 = 4120 \)[/tex]
- Residents who own a car: [tex]\( 3251 \)[/tex]
- Percentage of LA residents who own a car: [tex]\( \left( \frac{3251}{4120} \right) \times 100 \approx 78.91\% \)[/tex]
- NYC residents:
- Total residents surveyed: [tex]\( 1478 + 6182 = 7660 \)[/tex]
- Residents who own a car: [tex]\( 1478 \)[/tex]
- Percentage of NYC residents who own a car: [tex]\( \left( \frac{1478}{7660} \right) \times 100 \approx 19.30\% \)[/tex]
As 78.91% (LA) is greater than 19.30% (NYC), this statement is "True."
3. The total number of people in the poll who own a car is 4,120.
- Total number of residents in the poll who own a car is the sum of LA and NYC residents who own a car.
- Total: [tex]\( 3251 \text{ (LA)} + 1478 \text{ (NYC)} = 4729 \)[/tex]
Hence, the total number of people in the poll who own a car is 4729, not 4120. Therefore, this statement is "False."
4. More people in the poll own a car than do not own a car.
- Total number of residents who own a car: [tex]\( 4729 \)[/tex]
- Total number of residents who do not own a car: [tex]\( 7051 \)[/tex]
Since 4729 (own a car) is less than 7051 (do not own a car), this statement is "False."
### Conclusion
- The survey represents qualitative data: False
- There is a greater percentage of LA residents who own a car than NYC residents who do: True
- The total number of people in the poll who own a car is 4,120: False
- More people in the poll own a car than do not own a car: False
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Own a Car} & \text{Do Not Own a Car} & \text{Total} \\ \hline \text{LA residents} & 3,251 & 869 & 4,120 \\ \hline \text{NYC residents} & 1,478 & 6,182 & 7,660 \\ \hline \text{Total} & 4,729 & 7,051 & 11,780 \\ \hline \end{array} \][/tex]
### Breakdown of the Statements:
1. The survey represents quantitative data.
A survey is classified into qualitative or quantitative data. In this case, we are categorizing residents by whether they own a car or not. These categories are qualitative and not quantitative as we are dealing with categories, not numerical measurements. Therefore, this statement is "False."
2. There is a greater percentage of LA residents who own a car than NYC residents who do.
- LA residents:
- Total residents surveyed: [tex]\( 3251 + 869 = 4120 \)[/tex]
- Residents who own a car: [tex]\( 3251 \)[/tex]
- Percentage of LA residents who own a car: [tex]\( \left( \frac{3251}{4120} \right) \times 100 \approx 78.91\% \)[/tex]
- NYC residents:
- Total residents surveyed: [tex]\( 1478 + 6182 = 7660 \)[/tex]
- Residents who own a car: [tex]\( 1478 \)[/tex]
- Percentage of NYC residents who own a car: [tex]\( \left( \frac{1478}{7660} \right) \times 100 \approx 19.30\% \)[/tex]
As 78.91% (LA) is greater than 19.30% (NYC), this statement is "True."
3. The total number of people in the poll who own a car is 4,120.
- Total number of residents in the poll who own a car is the sum of LA and NYC residents who own a car.
- Total: [tex]\( 3251 \text{ (LA)} + 1478 \text{ (NYC)} = 4729 \)[/tex]
Hence, the total number of people in the poll who own a car is 4729, not 4120. Therefore, this statement is "False."
4. More people in the poll own a car than do not own a car.
- Total number of residents who own a car: [tex]\( 4729 \)[/tex]
- Total number of residents who do not own a car: [tex]\( 7051 \)[/tex]
Since 4729 (own a car) is less than 7051 (do not own a car), this statement is "False."
### Conclusion
- The survey represents qualitative data: False
- There is a greater percentage of LA residents who own a car than NYC residents who do: True
- The total number of people in the poll who own a car is 4,120: False
- More people in the poll own a car than do not own a car: False
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