Answered

A survey was taken of a random sampling of residents of New York City and Los Angeles to compare how many of them own a car.

Residents of Los Angeles and New York City Who Own a Car

\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Own a \\
car
\end{tabular} & \begin{tabular}{c}
Do not own a \\
car
\end{tabular} & Total \\
\hline LA residents & 3,251 & 869 & 4,120 \\
\hline NYC residents & 1,478 & 6,182 & 7,660 \\
\hline Total & 4,729 & 7,051 & 11,780 \\
\hline
\end{tabular}

Which statement about the two-way frequency table is true?

A. The survey represents quantitative data.

B. There is a greater percentage of LA residents who own a car than NYC residents who do.

C. The total number of people in the poll who own a car is 4,120.

D. More people in the poll own a car than do not own a car.



Answer :

GinnyAnswer
To determine which statement about the provided two-way frequency table is true, let's evaluate each statement individually using the data from the table.

### Step 1: Verify if the Survey Represents Quantitative Data
Quantitative data refers to numerical values that count or measure something. In this case, the data categorizes residents based on whether they own a car. This is categorical data, not quantitative, since it sorts individuals into two categories.

Conclusion:
- The survey does not represent quantitative data. This statement is false.

### Step 2: Calculate the Percentage of Residents Who Own a Car
We need to find the percentage of LA and NYC residents who own a car.

For LA Residents:
- Number of residents owning a car: 3,251
- Total number of LA residents surveyed: 4,120

[tex]\[ \text{Percentage of LA residents who own a car} = \left( \frac{3,251}{4,120} \right) \times 100 \approx 78.91\% \][/tex]

For NYC Residents:
- Number of residents owning a car: 1,478
- Total number of NYC residents surveyed: 7,660

[tex]\[ \text{Percentage of NYC residents who own a car} = \left( \frac{1,478}{7,660} \right) \times 100 \approx 19.30\% \][/tex]

Conclusion:
- There is a greater percentage of LA residents (78.91%) who own a car compared to NYC residents (19.30%). This statement is true.

### Step 3: Verify the Total Number of People in the Poll Who Own a Car
From the table:

Total Number of Residents Owning a Car:
[tex]\[ 3251 (\text{LA}) + 1478 (\text{NYC}) = 4,729 \][/tex]

Conclusion:
- The total number of people in the poll who own a car is not 4,120. This statement is false.

### Step 4: Compare the Number of People Who Own and Do Not Own a Car
Total Number of Residents Owning a Car:
[tex]\[ 4,729 \][/tex]

Total Number of Residents Not Owning a Car:
[tex]\[ 869 (\text{LA}) + 6,182 (\text{NYC}) = 7,051 \][/tex]

Conclusion:
- More people in the poll do not own a car (7,051) than those who own a car (4,729). This statement is false.

### Final Conclusion:
Based on the analysis, the only true statement is:
- There is a greater percentage of LA residents who own a car than NYC residents who do.