Construct a 95% confidence interval for the mean prices of homes with and withou
ID: 3054641 • Letter: C
Question
Construct a 95% confidence interval for the mean prices of homes with and without a fireplace. Compare the two intervals. Is there much overlap? What does the overlap tell you?
Price Living Area (SqFt) Bathrooms Bedrooms Fireplace Lot Size (Acres) Age (Yrs) $80,540 1380 1.5 2 0 0.13 0 $88,207 1480 1.5 3 0 0.07 14 $97,682 1548 1.5 3 0 0.31 85 $202,800 2250 2.5 4 0 0.31 2 $168,739 1620 2 3 0 0.3 0 $116,938 988 1 3 0 0.26 10 $159,313 1561 1.5 4 0 0.32 17 $45,004 960 1 2 0 0.54 11 $104,556 1673 2 2 0 0.15 18 $208,635 2714 3 4 0 0.55 1 $113,371 1177 1.5 3 0 0.17 36 $124,013 1524 1.5 3 0 0.71 180 $95,708 912 1.5 2 0 0.16 20 $139,104 1760 3 4 0 0.16 135 $110,770 911 1 2 0 0.12 114 $90,446 1256 1.5 3 0 0.21 19 $217,797 1386 1.5 2 0 0.23 92 $94,486 1150 1 3 0 0.34 45 $168,065 1016 2 2 0 0.01 41 $155,488 1747 2.5 3 0 0.36 1 $181,399 1842 1.5 3 0 0.53 8 $155,787 1540 1.5 3 0 0.43 16 $355,529 2186 2.5 3 0 1.4 12 $107,912 1308 1 3 0 0.46 26 $63,101 1628 1 2 0 0.06 124 $96,934 1480 1.5 3 0 0.08 19 $205,073 2501 2.5 4 0 0.07 0 $107,513 1008 1 3 0 0.22 38 $97,476 1219 1.5 2 0 0.01 19 $127,385 1416 1.5 3 0 0.37 11 $120,476 1120 2 3 0 0.73 7 $152,466 1600 2 4 0 0.46 35 $107,919 1056 2 2 0 0.52 7 $69,152 986 1 3 0 0.06 133 $200,793 1940 2 3 0 0.85 9 $95,708 912 1.5 2 0 0.16 20 $118,409 2128 2 4 0 1 7 $44,674 1214 1 3 0 0.14 103 $51,183 1144 1 3 0 0.64 15 $285,500 3328 2.5 4 1 0.35 0 $175,514 2475 2.5 4 1 0.59 35 $119,875 1512 1.5 4 1 1 61 $104,984 1144 1.5 3 1 0.52 44 $89,432 1132 1 2 1 0.16 25 $186,348 2011 2.5 4 1 0.37 14 $88,092 3944 1 4 1 1.64 185 $212,103 1400 2 3 1 0.98 25 $157,430 1092 1 3 1 0.28 41 $184,515 1472 1.5 4 1 0.7 3 $156,679 1911 1.5 4 1 0.43 35 $330,219 2576 2.5 3 1 0.55 31 $196,317 2359 2.5 4 1 0.61 1 $150,434 1611 2 4 1 0.17 83 $189,654 2320 2.5 4 1 0.65 16 $229,180 2310 2.5 4 1 1.4 3 $230,414 2623 2.5 4 1 0.53 0 $154,798 2470 2.5 4 1 0.34 26 $230,708 2548 2.5 3 1 0.36 3 $97,739 1276 2 2 1 0.17 26 $150,022 1632 2.5 4 1 0.5 30 $218,184 2655 2.5 4 1 0.37 1 $180,032 2066 2.5 4 1 0.41 32 $167,693 1876 2.5 3 1 0.34 1 $173,446 2124 2.5 3 1 0.14 0 $127,740 1480 2.5 3 1 0.03 16 $208,610 1752 2.5 3 1 0.74 10 $74,422 1708 1 2 1 0.87 39 $85,560 2068 1 4 1 1 104 $263,938 2641 2.5 4 1 0.34 3 $196,846 2144 2.5 3 1 0.92 19 $172,789 1812 2 3 1 1 16 $154,829 1440 2 2 1 0.61 66 $209,371 2076 2.5 3 1 0.62 13 $197,350 2500 3.5 4 1 0.21 1 $81,580 1336 1.5 2 1 0.35 20 $218,517 2038 2.5 3 1 0.98 13 $173,082 1656 2.5 3 1 0.35 18 $157,370 1656 1.5 3 1 0.33 19 $63,852 1536 1.5 4 1 0.46 30 $176,846 2249 2.5 4 1 0.59 1 $226,304 1921 2 3 1 1 0 $190,983 2088 2.5 4 1 0.49 22 $171,885 1536 2.5 3 1 0.72 7 $129,155 1260 1.5 2 1 0.06 27 $102,068 1172 2.5 3 1 0.85 73 $152,786 1578 2.5 3 1 0.46 11 $233,876 2434 2.5 4 1 1 20 $265,637 3030 2.5 4 1 0.5 1 $103,408 1034 1.5 2 1 0.21 14 $259,999 2577 2.5 4 1 0.77 1 $159,843 1350 1.5 2 1 0.68 1 $193,497 1948 2.5 3 1 1.13 13 $295,268 4534 2.5 6 1 5.08 15 $261,872 2380 2.5 3 1 0.95 9 $160,571 1294 1.5 3 1 0.32 17 $119,001 1506 1.5 3 1 0.46 24 $155,414 2310 2.5 4 1 0.6 38 $107,695 1802 2 4 1 0.97 56 $112,153 1270 1.5 3 1 0.09 18 $261,846 2772 2.5 4 1 0.29 0Explanation / Answer
following information has been generated using ms-excel
(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)
for without fireplace
95% confidence interval for population mean=mean±t(0.05/2, 38)*sd/sqrt(n)=129244.90±2.02*59317.97/sqrt(39)
for with fireplace
95% confidence interval for population mean=mean±t(0.05/2, 60)*sd/sqrt(n)=175168.44±2.00*59597.90/sqrt(61)
(second part) there is no overlap, as lower limit of without fireplace is more than upper limit of without fire place.
this imply that there is significant difference between with and without fire place with 95% confidence level or 5% level of significance
without Fireplace(0) with Fireplace(1) n= 39 61 mean= 129244.90 175168.44 sample sd= 59317.97 59597.90