Question: Construct a 95% confidence interval of the difference in population average house prices between houses with a basement (BASEMENT = 1) and houses without a
- 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 |
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