A real estate agent wants to know how many owners of homes worth over \$1,000,000 might be considering putting their home on the market in the next 12 months. He surveys 71 of them and finds that 18 of them are considering such a move. Are all the assumptions and conditions for finding the
sampling distribution of the proportion satisfied? Explain briefly.
Choose the correct answer below.
A. Yes; assuming the survey is random, they should be independent. The true proportion is about 0.25, and all other assumptions and conditions are met.
B. No; since some of the owners of \$1,000,000 homes might be friends, if one of them is choosing to sell his house, the other might follow. Therefore, the observations are not independent.
C. Yes; assuming the survey is random, they should be independent. Although the true proportion is not known so $np$ and $nq$ cannot be checked, with at least 10 successes and at least 10 failures, the Success/Failure Condition can be considered met.
D. No; since the owner of a \$1,000,000 home can make much more money selling his house than the average homeowner, the observations are not independent.