To determine which statement is true, we need to calculate the estimated number of households for each vehicle category in both towns based on the surveyed data.
Here’s how we do it:
- Total Households Surveyed: Both towns have 200 households surveyed.
- Total Number of Households in Each Town: Each town has 4,000 households.
Now we calculate the estimated number of households for each number of vehicles:
Estimates for Town A:
- One Vehicle: \( \frac{64}{200} \times 4000 = 1280 \)
- Two Vehicles: \( \frac{79}{200} \times 4000 = 1580 \)
- Three Vehicles: \( \frac{36}{200} \times 4000 = 720 \)
- None: \( \frac{21}{200} \times 4000 = 420 \)
Estimates for Town B:
- One Vehicle: \( \frac{66}{200} \times 4000 = 1320 \)
- Two Vehicles: \( \frac{79}{200} \times 4000 = 1580 \)
- Three Vehicles: \( \frac{27}{200} \times 4000 = 540 \)
- None: \( \frac{28}{200} \times 4000 = 560 \)
Now we summarize the estimated households based on the number of vehicles:
| Number of Vehicles | Town A | Town B | |--------------------|--------|--------| | One | 1280 | 1320 | | Two | 1580 | 1580 | | Three | 720 | 540 | | None | 420 | 560 |
Analysis of Statements:
A. The estimated number of households with two vehicles is higher in Town A than Town B.
False - The number is the same for both towns (1580).
B. The estimated number of households with three vehicles is the same for both towns.
False - Town A has 720, while Town B has 540.
C. The estimated number of households with two vehicles is higher in Town B than Town A.
False - The number is the same for both towns (1580).
D. The estimated number of households with two vehicles is the same for both towns.
True - Both have 1580 households estimated with two vehicles.
Therefore, the correct statement is D.