In Florida, real estate agents refer to homes having a swimmingpool as pool homes. In this case, Sunshine Pools Inc.markets and installs pools throughout the state of Florida. Thecompany wishes to estimate the percentage of a pool's cost that canbe 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 marketfor $20,000 more than the homeowner would get if the home did nothave 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 homesfrom all of the homes sold in a Florida city (over the last sixmonths) having a size between 2,000 and 3,500 square feet. For eachsampled home, the following data are collected:Price - selling price (in thousands ofdollars); Size - square footage;Bathrooms - the number of bathrooms;Rating - a niceness rating (expressed asan integer from 1 to 7 and assigned by a real estate agent); andPool - whether or not the home has a pool(1 = yes, 0 = no).

1. Your results in (4) show different mean selling prices forhomes with a pool and homes that do not have a pool. Can weconclude that the mean selling price for homes without a pool issignificantly lower than the mean selling price for homes with apool.

2. What about differences in average price among homes withdifferent number of bathrooms? Can we conclude that the differencesare significant? If so, which types of bedrooms have significantmean differences?

3. The president of the company told a potential buyer that onaverage, homes in the city sell for more than 258,000. Is thereevidence to support this claim?

4. (a) Is a home having a pool independent of the number ofbathrooms?

(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 thepercentage of homes with a pool for the entire city using thesample data he has. At the 95% confidence level, provide aninterval estimate, with an explanation, for the president.

6. Create a correlation matrix of the following metrics:Price, Size,Bathrooms, andRating. 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