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 within a mile of a park are randomly selected; 25 own a dog.
50 households with a front yard are randomly selected; 24 own a dog.
50 households are randomly selected from the town; 15 own a dog.
(b) there are 550 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 - representative survey

A random sample from the entire town is more representative. Households within a mile of a park or with a front - yard are subsets with specific characteristics. So, 50 households randomly selected from the town is the best - representative survey.

Step2: Calculate the proportion of dog - owning households in the sample

The proportion \(p\) of dog - owning households in the sample is \(p=\frac{15}{50}=0.3\)

Step3: Estimate the number of dog - owning households in the town

If there are \(N = 550\) households in the town, and using the proportion \(p\) from the sample, the estimated number of dog - owning households \(x\) is \(x = N\times p\). Substitute \(N = 550\) and \(p=0.3\) into the formula: \(x=550\times0.3\)

Answer:

(a) 50 households are randomly selected from the town; 15 own a dog.
(b) \(165\) households