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: Price - selling price (in thousands of dollars); Size - square footage; Bathrooms - the number of bathrooms; Rating - a niceness rating (expressed as an integer from 1 to 7 and assigned by a real estate agent); and Pool - whether or not the home has a pool (1 = yes, 0 = no).
1. Your results in (4) show different mean selling prices for homes with a pool and homes that do not have a pool. Can we conclude that the mean selling price for homes without a pool is significantly lower than the mean selling price for homes with a pool.
2. What about differences in average price among homes with different number of bathrooms? Can we conclude that the differences are significant? If so, which types of bedrooms have significant mean differences?
3. The president of the company told a potential buyer that on average, homes in the city sell for more than 258,000. Is there evidence to support this claim?
4. (a) Is a home having a pool independent of the number of bathrooms?
(b) What proportion of homes with a pool have 2, 2.5, 3, 3.5, and 4 bathrooms?
5. The president of the company would like to estimate the percentage of homes with a pool for the entire city using the sample data he has. At the 95% confidence level, provide an interval estimate, with an explanation, for the president.
6. Create a correlation matrix of the following metrics: Price, Size, Bathrooms, and Rating. Comment on the results.
Data Set:
Home | Price | Size | Bathrooms | Rating | Pool |
1 | 260.9 | 2666 | 2.5 | 7 | 0 |
2 | 337.3 | 3418 | 3.5 | 6 | 1 |
3 | 268.4 | 2945 | 2.0 | 5 | 1 |
4 | 242.2 | 2942 | 2.5 | 3 | 1 |
5 | 255.2 | 2798 | 3.0 | 3 | 1 |
6 | 205.7 | 2210 | 2.5 | 2 | 0 |
7 | 249.5 | 2209 | 2.0 | 7 | 0 |
8 | 193.6 | 2465 | 2.5 | 1 | 0 |
9 | 242.7 | 2955 | 2.0 | 4 | 1 |
10 | 244.5 | 2722 | 2.5 | 5 | 0 |
11 | 184.2 | 2590 | 2.5 | 1 | 0 |
12 | 325.7 | 3138 | 3.5 | 7 | 1 |
13 | 266.1 | 2713 | 2.0 | 7 | 0 |
14 | 166.0 | 2284 | 2.5 | 2 | 0 |
15 | 330.7 | 3140 | 3.5 | 6 | 1 |
16 | 289.1 | 3205 | 2.5 | 3 | 1 |
17 | 268.8 | 2721 | 2.5 | 6 | 1 |
18 | 276.7 | 3245 | 2.5 | 2 | 1 |
19 | 222.4 | 2464 | 3.0 | 3 | 1 |
20 | 241.5 | 2993 | 2.5 | 1 | 0 |
21 | 307.9 | 2647 | 3.5 | 6 | 1 |
22 | 223.5 | 2670 | 2.5 | 4 | 0 |
23 | 231.1 | 2895 | 2.5 | 3 | 0 |
24 | 216.5 | 2643 | 2.5 | 3 | 0 |
25 | 205.5 | 2915 | 2.0 | 1 | 0 |
26 | 258.3 | 2800 | 3.5 | 2 | 1 |
27 | 227.6 | 2557 | 2.5 | 3 | 1 |
28 | 255.4 | 2805 | 2.0 | 3 | 1 |
29 | 235.7 | 2878 | 2.5 | 4 | 0 |
30 | 285.1 | 2795 | 3.0 | 7 | 1 |
31 | 284.8 | 2748 | 2.5 | 7 | 1 |
32 | 193.7 | 2256 | 2.5 | 2 | 0 |
33 | 247.5 | 2659 | 2.5 | 2 | 1 |
34 | 274.8 | 3241 | 3.5 | 4 | 1 |
35 | 264.4 | 3166 | 3.0 | 3 | 1 |
36 | 204.1 | 2466 | 2.0 | 4 | 0 |
37 | 273.9 | 2945 | 2.5 | 5 | 1 |
38 | 238.5 | 2727 | 3.0 | 1 | 1 |
39 | 274.4 | 3141 | 4.0 | 4 | 1 |
40 | 259.6 | 2552 | 2.0 | 7 | 1 |
41 | 285.6 | 2761 | 3.0 | 6 | 1 |
42 | 216.1 | 2880 | 2.5 | 2 | 0 |
43 | 261.3 | 3426 | 3.0 | 1 | 1 |
44 | 236.4 | 2895 | 2.5 | 2 | 1 |
45 | 267.5 | 2726 | 3.0 | 7 | 0 |
46 | 220.2 | 2930 | 2.5 | 2 | 0 |
47 | 300.1 | 3013 | 2.5 | 6 | 1 |
48 | 260.0 | 2675 | 2.0 | 6 | 0 |
49 | 277.5 | 2874 | 3.5 | 6 | 1 |
50 | 274.9 | 2765 | 2.5 | 4 | 1 |
51 | 259.8 | 3020 | 3.5 | 2 | 1 |
52 | 235.0 | 2887 | 2.5 | 1 | 1 |
53 | 191.4 | 2032 | 2.0 | 3 | 0 |
54 | 228.5 | 2698 | 2.5 | 4 | 0 |
55 | 266.6 | 2847 | 3.0 | 2 | 1 |
56 | 233.0 | 2639 | 3.0 | 3 | 0 |
57 | 343.4 | 3431 | 4.0 | 5 | 1 |
58 | 334.0 | 3485 | 3.5 | 5 | 1 |
59 | 289.7 | 2991 | 2.5 | 6 | 1 |
60 | 228.4 | 2482 | 2.5 | 2 | 0 |
61 | 233.4 | 2712 | 2.5 | 1 | 1 |
62 | 275.7 | 3103 | 2.5 | 2 | 1 |
63 | 290.8 | 3124 | 2.5 | 3 | 1 |
64 | 230.8 | 2906 | 2.5 | 2 | 0 |
65 | 310.1 | 3398 | 4.0 | 4 | 1 |
66 | 247.9 | 3028 | 3.0 | 4 | 0 |
67 | 249.9 | 2761 | 2.0 | 5 | 0 |
68 | 220.5 | 2842 | 3.0 | 3 | 0 |
69 | 226.2 | 2666 | 2.5 | 6 | 0 |
70 | 313.7 | 2744 | 2.5 | 7 | 1 |
71 | 210.1 | 2508 | 2.5 | 4 | 0 |
72 | 244.9 | 2480 | 2.5 | 5 | 0 |
73 | 235.8 | 2986 | 2.5 | 4 | 0 |
74 | 263.2 | 2753 | 2.5 | 7 | 0 |
75 | 280.2 | 2522 | 2.5 | 6 | 1 |
76 | 290.8 | 2808 | 2.5 | 7 | 1 |
77 | 235.4 | 2616 | 2.5 | 3 | 0 |
78 | 190.3 | 2603 | 2.5 | 2 | 0 |
79 | 234.4 | 2804 | 2.5 | 4 | 0 |
80 | 238.7 | 2851 | 2.5 | 5 | 0 |
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