Question

town officials want to estimate the number of households that own a dog. answer the following.
(a) which of the following surveys would best represent the entire population of households?
50 households with a front yard are randomly selected; 26 own a dog.
50 households are randomly selected from the town; 16 own a dog.
50 households within a mile of a park are randomly selected; 23 own a dog.
(b) there are 450 households in the town. using your answer from part (a), estimate the number of households that own a dog.
□ households

Explanation:

Step1: Determine the best survey

A random sample from the entire town is more representative. The second option (50 households randomly selected from the town; 16 own a dog) is better as it's a random sample from the whole population compared to samples from a specific area (within a mile of a park) or with a specific feature (front - yard).

Step2: Calculate the proportion

The proportion of dog - owning households in the sample is \(p=\frac{16}{50}=0.32\)

Step3: Estimate the number

If there are \(N = 450\) households in the town, the estimated number of dog - owning households is \(n = N\times p\). Substitute \(N = 450\) and \(p=0.32\) into the formula: \(n=450\times0.32 = 144\)

Answer:

(a) 50 households are randomly selected from the town; 16 own a dog. (b) 144