Question

town officials want to estimate the number of households that own a dog. answer the following.
(a) which of the following surveys probably would best represent the entire population of households?
50 households with a front yard are randomly selected; 24 own a dog.
50 households within a mile of a park are randomly selected; 26 own a dog.
50 households are randomly selected from the town; 15 own a dog.
(b) there are 350 households in the town.
using your answer from part (a), estimate the number of households that own a dog.
\boxed{} households

Explanation:

Step1: Identify representative sample

A random sample of all town households best represents the entire population, so the third option is correct.

Step2: Calculate sample proportion

Find the proportion of dog-owning households in the sample.
$\text{Proportion} = \frac{15}{50} = 0.3$

Step3: Estimate population count

Multiply the proportion by total town households.
$350 \times 0.3 = 105$

Answer:

(a) 50 households are randomly selected from the town; 15 own a dog.
(b) 105 households