Questions: 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? 20 households within a mile of a park are randomly selected; 8 own a dog. 20 households with a garage are randomly selected; 12 own a dog. 20 households are randomly selected from the town; 7 own a dog. (b) There are 700 households in the town. Using your answer from part (a), estimate the number of households that own a dog. households

Solution Steps

To determine which survey best represents the entire population of households, we need to consider whether the sample is randomly selected and unbiased. The third option, where 20 households are randomly selected from the town, is the most representative because it does not introduce any bias (e.g., proximity to a park or having a garage). Thus, the third survey is the best choice.

From the third survey, we know that 7 out of 20 households own a dog. This gives a proportion of dog owners in the sample as: \[ \text{Proportion} = \frac{7}{20} = 0.35 \]

There are 700 households in the town. Using the proportion from the sample, we estimate the number of households that own a dog as: \[ \text{Estimated number of dog-owning households} = 700 \times 0.35 = 245 \]

Final Answer