(Hypothetical). A survey is carried out by the finance department to determine t

Question

(Hypothetical). A survey is carried out by the finance department to determine the distribution of household size in a certain city. They draw a simple random sample of 1,000 households. After several visits, the interviewers find people at home in only 653 of the sample households. Rather than face such a high non-response rate, the department draws a second batch of households, and uses the first 347 completed interviews in the second batch to bring the sample up to its planned strength of 1,000 households. The department counts 3,087 people in these 1,000 households, and estimates the average household size in the city to be about 3.1 persons. Is this estimate likely to be too low, too high, or about right? why?

Note: This question was answered already on Cramster but was graded very poorly.

Explanation / Answer

ok, this type of question does not have a standard answer. You need to make guesses sometimes, of course educated guesses. Don't worry too much about this type of questions, they are not usually given in exams. In this case, it is highly likely that the average occupants per household is overestimated. Note that you cannot say this for sure. This is only 1 sample. The reason is: If the household has fewer occupants, there is a higher probability of the house being empty, assuming that everyone is equally likely to stay at home or to go out. Hence, if they only count households with people at home, they are likely to miss out on households with fewer occupants. There are other possible reasoning. =) Try to think of one yourself! All the best!

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