Areal 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 proportionsatisfied? 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 israndom, they should be independent. the true proportion is about0.25, 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 bechecked, with at least 10 successes and at least 10 failures, thesuccess/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.