In Florida, real estate agents refer to homes having a swimming pool as pool homes. In this case, Sunshine Pools Inc. markets and installs pools throughout the state of Florida. The company wishes to estimate the percentage of a pool’s cost that can be recouped by a buyer when he or she sells the home. For instance, if a homeowner buys a pool for which the current purchase price is $ 30,000 and then sells the home in the current real estate market for $ 20,000 more than the homeowner would get if the home did not have a pool, the homeowner has recouped ( 20,000 30,000) 100% 66.67% of the pool’s cost.
To make this estimate, the company randomly selects 80 homes from all of the homes sold in a Florida city (over the last six months) having a size between 2,000 and 3,500 square feet. For each sampled home, the following data are collected: selling price ( in thousands of dollars); square footage; the number of bathrooms; a niceness rating ( expressed as an integer from 1 to 7 and assigned by a real estate agent); and whether or not the home has a pool (1 yes, 0 no). The data are given in Table 3.11. Figure 3.27 gives descriptive statistics for the 43 homes having a pool and for the 37 homes that do not have a pool.
a. Using Figure 3.27, compare the mean selling prices of the homes having a pool and the homes that do not have a pool.
b. Using these data, and assuming that the average current purchase price of the pools in the sample is $ 32,500, estimate the percentage of a pool’s cost that can be recouped when the home is sold.
c. The comparison you made in part (a) could be misleading. Noting that different homes have different square footages, numbers of bathrooms, and niceness ratings, explain why.