1. Construct a 95% confidence interval of the difference in population average house prices between houses with a basement (BASEMENT = 1) and houses without a basement (BASEMENT = 0). Assume variance are equal. Interpret the confidence interval. You have to show all the work in order to earn full credit. (5 points)

SQ_FT	BEDS	BATHS	HEAT	STYLE	GARAGE	BASEMENT	AGE	FIRE	PRICE	SCHOOL
1238	3	2	0	0	1	1	12	1	59.9	1
1707	3	2	1	0	2	0	13	1	64	0
1296	4	2	0	0	2	1	17	0	66.5	0
1320	3	2	0	0	2	1	11	1	66.5	0
1210	3	2	0	0	1	0	6	1	66.9	0
1296	3	2	0	0	2	1	17	1	68	0
1765	3	2	0	0	2	1	20	0	68.5	0
1725	4	3	0	0	2	1	12	0	69	0
1794	4	2	0	0	2	1	18	0	70.95	0
1294	3	2	0	0	2	0	13	1	71	0
1372	3	2	0	0	2	1	9	0	72.692	1
1162	3	2	0	0	1	0	8	1	72.801	0
1996	4	2	0	0	2	0	13	1	75.207	1
1764	4	2	1	0	2	1	13	1	76	0
1416	3	2	0	0	2	0	8	0	76	1
1730	4	2	0	0	2	0	15	1	77.5	0
1392	3	2	0	0	2	1	8	1	79.9	1
1664	3	3	0	0	2	0	11	1	79.9	0
1332	3	2	0	0	2	1	14	0	81	1
1752	3	3	0	0	2	0	18	1	82.8	0
2167	3	3	1	0	2	1	13	1	84.9	0
1664	3	2	0	0	2	0	9	1	85	0
1973	4	3	0	0	2	0	13	1	86	0
1384	3	2	0	0	2	0	5	1	89.28	0
1431	3	2	0	0	2	1	7	1	89.9	1
1950	5	3	0	0	2	0	13	1	90	0
1452	3	2	0	0	2	1	4	1	92	0
1829	3	2	0	0	2	0	10	1	92.439	1
1652	4	3	0	0	2	1	7	1	94.646	1
1516	3	2	0	0	2	1	10	1	97.293	1
1998	4	3	0	0	2	1	17	1	98.1	1
1984	4	3	0	0	2	1	9	1	98.149	0
1840	3	3	0	0	2	1	9	1	105	0
1823	4	3	0	0	2	1	3	1	110	1
2150	5	3	0	0	2	1	12	1	111.9	0
2096	3	3	0	0	2	1	9	1	113	1
2212	4	3	0	0	3	1	17	1	124	1
2375	4	3	0	0	2	1	11	1	133	1
2809	4	3	0	0	3	1	6	1	195	0
912	4	2	0	1	2	1	19	1	59	0
816	3	2	0	1	2	1	19	0	61.5	0
1008	5	2	0	1	2	1	17	0	63.5	0
912	4	2	0	1	2	1	16	1	66.95	1
1008	5	2	0	1	2	1	17	1	68	0
838	4	2	0	1	1	1	11	0	68.694	1
1008	4	3	0	1	2	1	19	1	69	0
1120	3	2	0	1	2	1	11	1	70.452	1
1242	4	3	0	1	2	1	12	0	75	0
912	4	2	0	1	2	1	18	1	76.9	1
1316	3	2	0	1	2	1	8	1	83	0
1490	3	2	0	1	2	1	13	1	88	0
1118	4	3	0	1	2	1	16	1	88.879	1
1278	3	2	0	1	2	1	11	1	89.347	0
1490	3	2	0	1	2	1	10	1	89.7	1
1418	4	2	0	1	2	1	14	1	90	1
1250	4	3	0	1	2	1	17	1	90.8	1
1881	4	3	0	1	2	1	9	1	91.5	1
1355	3	2	0	1	2	1	7	1	95	1
1518	3	2	0	1	2	1	22	0	98	1
1606	4	3	0	1	2	1	13	1	99.5	0
2124	3	2	0	1	2	1	14	1	107	0
2099	4	3	0	1	2	1	13	1	113.75	1
2232	5	3	0	1	2	1	9	1	125	1
1608	5	3	0	1	3	1	13	1	132	1
1320	3	2	0	2	2	1	13	1	76	1
1680	3	3	0	2	2	0	7	1	79.9	1
1434	3	3	0	2	2	1	12	1	79.9	1
1664	3	2	0	2	2	1	7	1	85	1
1379	3	2	0	2	2	1	8	1	87.158	1
1634	3	3	0	2	2	1	10	1	87.2	1
1400	3	3	0	2	2	0	1	1	91.5	1
1664	4	4	0	2	2	1	16	1	91.5	1
1548	3	3	0	2	2	1	8	1	92.5	1
2040	4	3	0	2	2	1	15	1	93.5	0
1792	4	3	0	2	2	1	9	1	94	1
1865	3	3	0	2	2	1	12	1	96.7	0
1833	3	3	0	2	2	1	7	1	97.4	1
1627	3	3	0	2	2	1	3	1	98.5	1
2198	4	3	0	2	2	1	12	1	99	0
1707	3	3	0	2	2	1	12	1	99	0
2096	3	3	0	2	2	1	7	1	102.4	1
2004	4	3	0	2	2	1	13	1	104	0
1818	4	3	0	2	2	1	19	1	107	1
1935	3	3	0	2	2	1	11	1	107.9	1
2381	3	3	0	2	2	0	17	1	109	1
1977	3	3	0	2	2	1	9	1	110	1
2317	5	3	0	2	2	1	9	1	110.5	1
2072	4	3	0	2	2	1	11	1	112	1
2108	3	3	0	2	2	1	7	1	112.9	0
2060	4	4	0	2	2	1	9	1	113.6	1
2064	3	3	0	2	2	1	5	1	114.5	1
2148	5	4	0	2	2	1	8	1	114.7	1
2170	6	4	0	2	2	1	21	1	115	1
1984	4	3	1	2	2	1	11	1	121	1
2130	4	3	0	2	2	1	20	1	121	1
2049	4	3	0	2	2	1	19	1	125	1
2035	3	3	0	2	3	1	6	1	128	1
2264	3	3	0	2	3	1	7	1	130	1
2264	3	3	0	2	3	1	10	1	131	1
2362	4	3	0	2	2	1	6	1	132	0
2262	5	3	0	2	2	1	12	1	132.5	1
2353	4	3	0	2	2	1	5	1	132.5	0
2298	3	3	0	2	3	1	2	1	144.5	1
2282	4	3	0	2	2	1	9	1	150.577	1
2542	4	3	0	2	2	1	6	1	153.8	1
2380	4	3	0	2	2	1	6	1	155	1
2505	4	3	0	2	2	1	7	1	156.9	1
2804	4	3	0	2	3	1	1	1	192	1