Town officials want to estimate the number of households that own a dog

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?

1. 25 households are randomly selected from the town; 7 own a dog.
2. 25 households with a backyard are randomly selected; 11 own a dog.
3. 25 households within a mile of a park are randomly selected; 12 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

Answer 1

A classic Algebra question!

First and foremost, let's address the quality of the samples -- that is, which style of house should we focus on. When considering the entire population of households, we want the most general descriptor. If we look at only houses with backyards, or within a certain distance from a park, we would greatly limit the number of houses we could consider, because it's just too specific. To get the most accurate estimate, we would choose option 1 -- "25 households are randomly selected from the town; 7 own a dog.".

Next, we will discuss how we can figure out the number of houses with dogs. With the most general and, therefore, most accurate approximation of the houses in the town, we can simply divide 7 dogs/ 25 houses, which gives us .28, or 28%. So, just over a quarter of the households own dogs. Finally, we multiple 450, the total number of houses in the town, by .28. By this math, we can safely estimate that 126 of the households in the town own dogs.

Answer 2

Hello!

I'm not a huge fan of the question, it seems to be too subjective depending on who you ask. But if I had to chose the one that I felt was the most correct, it would be the first one. Since the other two choices are only focused on one specific group of homes (based on backyard or location) and exclude all others.

We can then set up a proportion; 7/25 = x/450.

Cross multiply; 25x = 3150

Divide by 25 and get x = 126.

So if you choose the first option, that would me 126 homes in the entire town own a dog.