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 78 of them and finds that 20 of them are considering such a move. Are all the assumptions and conditions for finding the sampling distribution of the proportion​satisfied? Explain briefly.
a) ​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.
b) ​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.
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.