Certainly! Let's analyze the given two-way frequency table and the provided statements:
| | Own a car | Do not own a car | Total |
|----|-----------|------------------|--------|
| LA residents | 3,251 | 869 | 4,120 |
| NYC residents | 1,478 | 6,182 | 7,660 |
| Total | 4,729 | 7,051 | 11,780|
We need to determine which statement is true based on the data from this table. Let's break down the analysis step by step.
1. Statement: "The survey represents quantitative data."
- Explanation: Quantitative data involves quantities and numbers where mathematical operations can be performed on the values. However, this survey counts categories such as "Own a car" and "Do not own a car," which are categorical data, not quantitative. This statement is false.
2. Statement: "There is a greater percentage of LA residents who own a car than NYC residents who do."
- Calculations:
- Percentage of LA residents who own a car:
[tex]\[ \left(\frac{3,251}{4,120}\right) \times 100 \approx 78.89\% \][/tex]
- Percentage of NYC residents who own a car:
[tex]\[ \left(\frac{1,478}{7,660}\right) \times 100 \approx 19.29\% \][/tex]
- Since [tex]\(78.89\% > 19.29\%\)[/tex], it is indeed true that there is a greater percentage of LA residents who own a car compared to NYC residents. This statement is true.
3. Statement: "The total number of people in the poll who own a car is 4,120."
- Explanation: According to the data, the total number of people who own a car is the sum of LA and NYC residents:
[tex]\[ 3,251 + 1,478 = 4,729 \][/tex]
- This statement is false since the actual total is 4,729, not 4,120.
4. Statement: "More people in the poll own a car than do not own a car."
- Calculations: Compare the total number of people who own a car with those who do not:
- People who own a car: 4,729
- People who do not own a car: 7,051
- Since [tex]\(7,051 > 4,729\)[/tex], more people do not own a car than own a car. This statement is false.
Thus, the analysis verifies the following:
- The survey does not represent quantitative data.
- There is a greater percentage of LA residents who own a car than NYC residents who do.
- The total number of people in the poll who own a car is not 4,120.
- More people in the poll do not own a car compared to those who own a car.
The correct true statement from the given options is:
- "There is a greater percentage of LA residents who own a car than NYC residents who do."
