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?

A. 20 households with a front yard are randomly selected; 10 own a dog.

B. 20 households within a mile of a park are randomly selected; 12 own a dog.

C. 20 households are randomly selected from the town; 9 own a dog.

Answer the following.
There are 300 households in the town.

Estimate how many households that own a dog

__ households

probably C

9/20 * 300 = _____

Well, let's first eliminate option C because it only represents 20 households out of the entire town. That's like trying to capture the essence of a clown with just one floppy shoe!

Now, for options A and B, they both randomly select 20 households, but the conditions differ. Option A selects households with a front yard, while option B selects households within a mile of a park. It seems like option B includes a wider range of households, so it might be a better representation of the entire population.

Now, let me grab my juggling balls and calculate an estimate for you. If there are 300 households in the town, and option B says that 12 out of 20 households own a dog, we can set up a proportion to find the estimated number of dog-owning households.

12/20 = x/300

Now, we just cross-multiply and solve for x. Drumroll, please...

12 * 300 = 20 * x

x = 1,800/20

x = 90

So, estimated number of households that own a dog would be 90 households. Woof!

To estimate the number of households that own a dog, we need to select a survey that best represents the entire population of households.

By comparing the three options, we can see that Option B seems to be the most representative. Option B involves randomly selecting 20 households within a mile of a park, and out of those households, 12 own a dog.

Using this information, we can calculate the estimated number of households that own a dog in the entire population as follows:

Number of households in the sample: 20
Number of households in the sample that own a dog: 12

Now, let's calculate the estimated number of households that own a dog in the entire population of 300 households using a proportion:

(12 / 20) = (x / 300)

Cross multiplying, we have:

20x = 12 * 300
20x = 3600

Dividing both sides by 20:

x = 3600 / 20
x = 180

Therefore, the estimate is that there are 180 households in the town that own a dog.

To estimate the number of households that own a dog in the town, we need to choose the survey that best represents the entire population of households.

Let's evaluate the options:

A. 20 households with a front yard are randomly selected; 10 own a dog.
This survey only considers households with a front yard, which might not accurately represent the entire population of households. Moreover, the sample size is small, making it less reliable for estimating the entire population.

B. 20 households within a mile of a park are randomly selected; 12 own a dog.
This survey focuses on households located near a park. While this criterion might be relevant for dog ownership, it still may not capture the diversity of households in the entire town. The sample size is still relatively small.

C. 20 households are randomly selected from the town; 9 own a dog.
This survey randomly selects households from the entire town. This approach is more likely to represent the entire population and provide a better estimate of the number of households that own a dog. However, the sample size is still relatively small.

Since all the surveys have relatively small sample sizes, option C, which randomly selects households from the entire town, is the most appropriate choice. This survey offers the most generalizable results.

To estimate the number of households that own a dog, we can use the proportion of households that own a dog in the survey and apply it to the total number of households in the town:

Number of households that own a dog = (Proportion of households that own a dog in the survey) * (Total number of households in the town)

For example, if 9 out of 20 randomly selected households own a dog in the survey, we can estimate the number of households that own a dog:

Number of households that own a dog = (9/20) * 300 = 135 households

Therefore, an estimated 135 households in the town own a dog.