Exercise 3: Two-Sample Tests of Hypothesis

For the following exercise, state the null and alternative hypotheses, determine the correct test statistic, formulate the decision rule, and interpret the results. Summarize the questions in a brief paragraph.

• (a) At the .05 significance level, is a difference in the mean selling Price (market price in dollars) of homes with a pool and homes without a pool?
• (b) At the .05 significance level, is a difference in the mean Price (market price in dollars) of homes with an attached garage and homes without an attached garage?

Data

SYM-506 North Valley Real Estate Case Study Data Set
record	Agent	Price	Size	Bedrooms	Baths	Pool (yes is 1)	Garage (Yes is 1)	Days	Township	Mortgage type	Years	FICO	Default (Yes is 1)
1	Marty	$206,424.00	1820	2	1.5	1	1	33	2	Fixed	2	824	0
2	Rose	$346,150.00	3010	3	2	0	0	36	4	Fixed	9	820	0
3	Carter	$372,360.00	3210	4	3	0	1	21	2	Fixed	18	819	0
4	Peterson	$310,622.00	3330	3	2.5	1	0	26	3	Fixed	17	817	0
5	Carter	$496,100.00	4510	6	4.5	0	1	13	4	Fixed	17	816	0
6	Peterson	$294,086.00	3440	4	3	1	1	31	4	Fixed	19	813	0
7	Carter	$228,810.00	2630	4	2.5	0	1	39	4	Adjustable	10	813	0
8	Isaacs	$384,420.00	4470	5	3.5	0	1	26	2	Fixed	6	812	0
9	Peterson	$416,120.00	4040	5	3.5	0	1	26	4	Fixed	3	810	0
10	Isaacs	$487,494.00	4380	6	4	1	1	32	3	Fixed	6	808	0
11	Rose	$448,800.00	5280	6	4	0	1	35	4	Fixed	8	806	1
12	Peterson	$388,960.00	4420	4	3	0	1	50	2	Adjustable	9	805	1
13	Marty	$335,610.00	2970	3	2.5	0	1	25	3	Adjustable	9	801	1
14	Rose	$276,000.00	2300	2	1.5	0	0	34	1	Fixed	20	798	0
15	Rose	$346,421.00	2970	4	3	1	1	17	3	Adjustable	10	795	0
16	Isaacs	$453,913.00	3660	6	4	1	1	12	3	Fixed	18	792	0
17	Carter	$376,146.00	3290	5	3.5	1	1	28	2	Adjustable	9	792	1
18	Peterson	$694,430.00	5900	5	3.5	1	1	36	3	Adjustable	10	788	0
19	Rose	$251,269.00	2050	3	2	1	1	38	3	Fixed	16	786	0
20	Rose	$547,596.00	4920	6	4.5	1	1	37	5	Fixed	2	785	0
21	Marty	$214,910.00	1950	2	1.5	1	0	20	4	Fixed	6	784	0
22	Rose	$188,799.00	1950	2	1.5	1	0	52	1	Fixed	10	782	0
23	Carter	$459,950.00	4680	4	3	1	1	31	4	Fixed	8	781	0
24	Isaacs	$264,160.00	2540	3	2.5	0	1	40	1	Fixed	18	780	0
25	Carter	$393,557.00	3180	4	3	1	1	54	1	Fixed	20	776	0
26	Isaacs	$478,675.00	4660	5	3.5	1	1	26	5	Adjustable	9	773	0
27	Carter	$384,020.00	4220	5	3.5	0	1	23	4	Adjustable	9	772	1
28	Marty	$313,200.00	3600	4	3	0	1	31	3	Fixed	19	772	0
29	Isaacs	$274,482.00	2990	3	2	1	0	37	3	Fixed	5	769	0
30	Marty	$167,962.00	1920	2	1.5	1	1	31	5	Fixed	6	769	0
31	Isaacs	$175,823.00	1970	2	1.5	1	0	28	5	Adjustable	9	766	1
32	Isaacs	$226,498.00	2520	4	3	1	1	28	3	Fixed	8	763	1
33	Carter	$316,827.00	3150	4	3	1	1	22	4	Fixed	2	759	1
34	Carter	$189,984.00	1550	2	1.5	1	0	22	2	Fixed	17	758	0
35	Marty	$366,350.00	3090	3	2	1	1	23	3	Fixed	5	754	1
36	Isaacs	$416,160.00	4080	4	3	0	1	25	4	Fixed	12	753	0
37	Isaacs	$308,000.00	3500	4	3	0	1	37	2	Fixed	18	752	0
38	Rose	$294,357.00	2620	4	3	1	1	15	4	Fixed	10	751	0
39	Carter	$337,144.00	2790	4	3	1	1	19	3	Fixed	15	749	0
40	Peterson	$299,730.00	2910	3	2	0	0	31	2	Fixed	13	748	0
41	Rose	$445,740.00	4370	4	3	0	1	19	3	Fixed	5	746	0
42	Rose	$410,592.00	4200	4	3	1	1	27	1	Adjustable	9	741	1
43	Peterson	$667,732.00	5570	5	3.5	1	1	29	5	Fixed	4	740	0
44	Rose	$523,584.00	5050	6	4	1	1	19	5	Adjustable	10	739	0
45	Marty	$336,000.00	3360	3	2	0	0	32	3	Fixed	6	737	0
46	Marty	$202,598.00	2270	3	2	1	0	28	1	Fixed	10	737	0
47	Marty	$326,695.00	2830	3	2.5	1	0	30	4	Fixed	8	736	0
48	Rose	$321,320.00	2770	3	2	0	1	23	4	Fixed	6	736	0
49	Isaacs	$246,820.00	2870	4	3	0	1	27	5	Fixed	13	735	0
50	Isaacs	$546,084.00	5910	6	4	1	1	35	5	Adjustable	10	731	0
51	Isaacs	$793,084.00	6800	8	5.5	1	1	27	4	Fixed	6	729	0
52	Isaacs	$174,528.00	1600	2	1.5	1	0	39	2	Fixed	15	728	0
53	Peterson	$392,554.00	3970	4	3	1	1	30	4	Fixed	17	726	0
54	Peterson	$263,160.00	3060	3	2	0	1	26	3	Fixed	10	726	0
55	Rose	$237,120.00	1900	2	1.5	1	0	14	3	Fixed	18	723	0
56	Carter	$225,750.00	2150	2	1.5	1	1	27	2	Fixed	15	715	0
57	Isaacs	$848,420.00	7190	6	4	0	1	49	1	Fixed	5	710	0
58	Carter	$371,956.00	3110	5	3.5	1	1	29	5	Fixed	8	710	0
59	Carter	$404,538.00	3290	5	3.5	1	1	24	2	Fixed	14	707	0
60	Rose	$250,090.00	2810	4	3	0	1	18	5	Fixed	11	704	0
61	Peterson	$369,978.00	3830	4	2.5	1	1	27	4	Fixed	10	703	0
62	Peterson	$209,292.00	1630	2	1.5	1	0	18	3	Fixed	10	701	0
63	Isaacs	$190,032.00	1850	2	1.5	1	1	30	4	Adjustable	2	675	0
64	Isaacs	$216,720.00	2520	3	2.5	0	0	2	4	Adjustable	5	674	1
65	Marty	$323,417.00	3220	4	3	1	1	22	4	Adjustable	2	673	0
66	Isaacs	$316,210.00	3070	3	2	0	0	30	1	Adjustable	1	673	0
67	Peterson	$226,054.00	2090	2	1.5	1	1	28	1	Adjustable	6	670	0
68	Marty	$183,920.00	2090	3	2	0	0	30	2	Adjustable	8	669	1
69	Rose	$248,400.00	2300	3	2.5	1	1	50	2	Adjustable	4	667	0
70	Isaacs	$466,560.00	5760	5	3.5	0	1	42	4	Adjustable	3	665	0
71	Rose	$667,212.00	6110	6	4	1	1	21	3	Adjustable	8	662	1
72	Peterson	$362,710.00	4370	4	2.5	0	1	24	1	Adjustable	2	656	0
73	Rose	$265,440.00	3160	5	3.5	1	1	22	5	Adjustable	3	653	0
74	Rose	$706,596.00	6600	7	5	1	1	40	3	Adjustable	7	652	1
75	Marty	$293,700.00	3300	3	2	0	0	14	4	Adjustable	7	647	1
76	Marty	$199,448.00	2330	2	1.5	1	1	25	3	Adjustable	5	644	1
77	Carter	$369,533.00	4230	4	3	1	1	32	2	Adjustable	2	642	0
78	Marty	$230,121.00	2030	2	1.5	1	0	21	2	Adjustable	3	639	0
79	Marty	$169,000.00	1690	2	1.5	0	0	20	1	Adjustable	7	639	1
80	Peterson	$190,291.00	2040	2	1.5	1	1	31	4	Adjustable	6	631	1
81	Rose	$393,584.00	4660	4	3	1	1	34	3	Adjustable	7	630	1
82	Marty	$363,792.00	2860	3	2.5	1	1	48	5	Adjustable	3	626	0
83	Carter	$360,960.00	3840	6	4.5	0	1	32	2	Adjustable	5	626	1
84	Carter	$310,877.00	3180	3	2	1	1	40	1	Adjustable	6	624	1
85	Peterson	$919,480.00	7670	8	5.5	1	1	30	4	Adjustable	1	623	0
86	Carter	$392,904.00	3400	3	2	1	0	40	2	Adjustable	8	618	1
87	Carter	$200,928.00	1840	2	1.5	1	1	36	4	Adjustable	3	618	1
88	Carter	$537,900.00	4890	6	4	0	1	23	1	Adjustable	7	614	0
89	Rose	$258,120.00	2390	3	2.5	0	1	23	1	Adjustable	6	614	1
90	Carter	$558,342.00	6160	6	4	1	1	24	3	Adjustable	7	613	0
91	Marty	$302,720.00	3440	4	2.5	0	1	38	3	Adjustable	3	609	1
92	Isaacs	$240,115.00	2220	2	1.5	1	0	39	5	Adjustable	1	609	0
93	Carter	$793,656.00	6530	7	5	1	1	53	4	Adjustable	3	605	1
94	Peterson	$218,862.00	1930	2	1.5	1	0	58	4	Adjustable	1	604	0
95	Peterson	$383,081.00	3510	3	2	1	1	27	2	Adjustable	6	601	1
96	Marty	$351,520.00	3380	3	2	0	1	35	2	Adjustable	8	599	1
97	Peterson	$841,491.00	7030	6	4	1	1	50	4	Adjustable	8	596	1
98	Marty	$336,300.00	2850	3	2.5	0	0	28	1	Adjustable	6	595	1
99	Isaacs	$312,863.00	3750	6	4	1	1	12	4	Adjustable	2	595	0
100	Carter	$275,033.00	3060	3	2	1	1	27	3	Adjustable	3	593	0
101	Peterson	$229,990.00	2110	2	1.5	0	0	37	3	Adjustable	6	591	1
102	Isaacs	$195,257.00	2130	2	1.5	1	0	11	5	Adjustable	8	591	1
103	Marty	$194,238.00	1650	2	1.5	1	1	30	2	Adjustable	7	590	1
104	Peterson	$348,528.00	2740	4	3	1	1	27	5	Adjustable	3	584	1
105	Peterson	$241,920.00	2240	2	1.5	0	1	34	5	Adjustable	8	583	1