Question 1177030: 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?
20 households within a mile of a park are randomly selected; 10 own a dog.
20 households are randomly selected from the town; 7 own a dog.
20 households with a garage are randomly selected; 11 own a dog.
(b)There are 1000 households in the town.
Using your answer from part (a), estimate the number of households that own a dog.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
If you pick households that are within a mile of the park, then you ignore households that are more than a mile away from the park. The same idea applies to those with garages vs those who don't have garages. In either of these situations, we aren't making a truly representative sample of the population. Consider that this town has vastly more households without garages than those who do have garages. If we go with the garage option, then we leave out a large chunk of the population.
The best scenario is to randomly select households without any prior restrictions or qualifications. Perhaps we should number each house, then use a random number generator to select the 20 households. So that means we'll go with "20 households are randomly selected from the town; 7 own a dog." as the final answer.
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Part (b)
Refer to the answer of part (a). In the sample, we had 7 households that owned a dog out of 20 households total. This is 7/20 = 0.35 = 35% of the sample.
If the sample is unbiased and representative of the population, then we should expect roughly 35% of the population owns a dog. Think of the sample as a miniaturized version of the population.
That means we expect around 0.35*1000 = 350 households to own a dog.
Answer: 350 households
This is of course an estimate and not a guaranteed true count.
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