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 & Own a car & Do not own a car & 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
Let's analyze the data from the survey and the possible true statements one by one.

1. The survey represents quantitative data.

This statement is not correct. The survey data is categorical (qualitative), as it categorizes residents based on whether they own a car or not.

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

To determine this, we'll calculate the percentages:

- For LA residents:
- [tex]\( \text{Number of LA residents who own a car} = 3251 \)[/tex]
- [tex]\( \text{Total number of LA residents} = 4120 \)[/tex]
- [tex]\( \text{Percentage of LA residents who own a car} = \left(\frac{3251}{4120}\right) \times 100 \approx 78.91\% \)[/tex]

- For NYC residents:
- [tex]\( \text{Number of NYC residents who own a car} = 1478 \)[/tex]
- [tex]\( \text{Total number of NYC residents} = 7660 \)[/tex]
- [tex]\( \text{Percentage of NYC residents who own a car} = \left(\frac{1478}{7660}\right) \times 100 \approx 19.30\% \)[/tex]

Comparing these percentages, [tex]\( 78.91\% \)[/tex] of LA residents own a car, while only [tex]\( 19.30\% \)[/tex] of NYC residents do, which indicates this statement is correct.

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

Reviewing the totals:

- [tex]\( \text{Total number of people in LA who own a car} = 3251 \)[/tex]
- [tex]\( \text{Total number of people in NYC who own a car} = 1478 \)[/tex]
- [tex]\( \text{Total number of people who own a car} = 3251 + 1478 = 4729 \)[/tex]

This means the total number of people in the poll who own a car is 4729. Therefore, this statement is incorrect.

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

Let's compare the total numbers:

- [tex]\( \text{Total number of people who own a car} = 4729 \)[/tex]
- [tex]\( \text{Total number of people who do not own a car} = 7051 \)[/tex]

Clearly, [tex]\( 7051 > 4729 \)[/tex], so more people in the poll do not own a car. Hence, this statement is incorrect.

Conclusion:
The only true statement is:
- There is a greater percentage of LA residents who own a car than NYC residents who do.