Homework SoursePrice 3 Refer to the Real Estate data which report informati
Price
3
Refer to the Real Estate data, which report information on homes in the Goodyear, Arizona, area during last year.
a. A recent article in the Arizona Republic indicated that the mean selling price of the homes in the area is more than $220,000. Can we conclude that the mean selling price in the Goodyear, AZ area is more than $220,000? Use the 0.01 significance level. What is the p-value?
b. The same article reported the mean size was more than 2,100 square feet. Can we conclude that the man size of homes sold in the Goodyear, AZ, area is more than 2,100 square feet? Use the 0.01 significance level. What is the p-value?
c. Determine the proportion of homes that have an attached garage. At the 0.05 significance level, can we conclude that more than 60% of the homes sold in the Goodyear, AZ, area had an attached garage? What is the p-value?
d. Determine the proportion of homes that have a pool. At the 0.05 significance level, can we conclude that more than 60% of the homes sold in the Goodyear, AZ, area had a pool? What is the p-value?
| Price | Bedrooms | Size | Pool | Distance | Twnship | Garage | Baths |
| 263.1 | 4 | 2300 | 0 | 17 | 5 | 1 | 2 |
| 182.4 | 4 | 2100 | 1 | 19 | 4 | 0 | 2 |
| 242.1 | 3 | 2300 | 1 | 12 | 3 | 0 | 2 |
| 213.6 | 2 | 2200 | 1 | 16 | 2 | 0 | 2.5 |
| 139.9 | 2 | 2100 | 1 | 28 | 1 | 0 | 1.5 |
| 245.4 | 2 | 2100 | 0 | 12 | 1 | 1 | 2 |
| 327.2 | 6 | 2500 | 1 | 15 | 3 | 1 | 2 |
| 271.8 | 2 | 2100 | 1 | 9 | 2 | 1 | 2.5 |
| 221.1 | 3 | 2300 | 0 | 18 | 1 | 0 | 1.5 |
| 266.6 | 4 | 2400 | 1 | 13 | 4 | 1 | 2 |
| 292.4 | 4 | 2100 | 1 | 14 | 3 | 1 | 2 |
| 209 | 2 | 1700 | 1 | 8 | 4 | 1 | 1.5 |
| 270.8 | 6 | 2500 | 1 | 7 | 4 | 1 | 2 |
| 246.1 | 4 | 2100 | 1 | 18 | 3 | 1 | 2 |
| 194.4 | 2 | 2300 | 1 | 11 | 3 | 0 | 2 |
| 281.3 | 3 | 2100 | 1 | 16 | 2 | 1 | 2 |
| 172.7 | 4 | 2200 | 0 | 16 | 3 | 0 | 2 |
| 207.5 | 5 | 2300 | 0 | 21 | 4 | 0 | 2.5 |
| 198.9 | 3 | 2200 | 0 | 10 | 4 | 1 | 2 |
| 209.3 | 6 | 1900 | 0 | 15 | 4 | 1 | 2 |
| 252.3 | 4 | 2600 | 1 | 8 | 4 | 1 | 2 |
| 192.9 | 4 | 1900 | 0 | 14 | 2 | 1 | 2.5 |
| 209.3 | 5 | 2100 | 1 | 20 | 5 | 0 | 1.5 |
| 345.3 | 8 | 2600 | 1 | 9 | 4 | 1 | 2 |
| 326.3 | 6 | 2100 | 1 | 11 | 5 | 1 | 3 |
| 173.1 | 2 | 2200 | 0 | 21 | 5 | 1 | 1.5 |
| 187 | 2 | 1900 | 1 | 26 | 4 | 0 | 2 |
| 257.2 | 2 | 2100 | 1 | 9 | 4 | 1 | 2 |
| 233 | 3 | 2200 | 1 | 14 | 3 | 1 | 1.5 |
| 180.4 | 2 | 2000 | 1 | 11 | 5 | 0 | 2 |
| 234 | 2 | 1700 | 1 | 19 | 3 | 1 | 2 |
| 207.1 | 2 | 2000 | 1 | 11 | 5 | 1 | 2 |
| 247.7 | 5 | 2400 | 1 | 16 | 2 | 1 | 2 |
| 166.2 | 3 | 2000 | 0 | 16 | 2 | 1 | 2 |
| 177.1 | 2 | 1900 | 1 | 10 | 5 | 1 | 2 |
| 182.7 | 4 | 2000 | 0 | 14 | 4 | 0 | 2.5 |
| 216 | 4 | 2300 | 1 | 19 | 2 | 0 | 2 |
| 312.1 | 6 | 2600 | 1 | 7 | 5 | 1 | 2.5 |
| 199.8 | 3 | 2100 | 1 | 19 | 3 | 1 | 2 |
| 273.2 | 5 | 2200 | 1 | 16 | 2 | 1 | 3 |
| 206 | 3 | 2100 | 0 | 9 | 3 | 0 | 1.5 |
| 232.2 | 3 | 1900 | 0 | 16 | 1 | 1 | 1.5 |
| 198.3 | 4 | 2100 | 0 | 19 | 1 | 1 | 1.5 |
| 205.1 | 3 | 2000 | 0 | 20 | 4 | 0 | 2 |
| 175.6 | 4 | 2300 | 0 | 24 | 4 | 1 | 2 |
| 307.8 | 3 | 2400 | 0 | 21 | 2 | 1 | 3 |
| 269.2 | 5 | 2200 | 1 | 8 | 5 | 1 | 3 |
| 224.8 | 3 | 2200 | 1 | 17 | 1 | 1 | 2.5 |
| 171.6 | 3 | 2000 | 0 | 16 | 4 | 0 | 2 |
| 216.8 | 3 | 2200 | 1 | 15 | 1 | 1 | 2 |
| 192.6 | 6 | 2200 | 0 | 14 | 1 | 0 | 2 |
| 236.4 | 5 | 2200 | 1 | 20 | 3 | 1 | 2 |
| 172.4 | 3 | 2200 | 1 | 23 | 3 | 0 | 2 |
| 251.4 | 3 | 1900 | 1 | 12 | 2 | 1 | 2 |
| 246 | 6 | 2300 | 1 | 7 | 3 | 1 | 3 |
| 147.4 | 6 | 1700 | 0 | 12 | 1 | 0 | 2 |
| 176 | 4 | 2200 | 1 | 15 | 1 | 1 | 2 |
| 228.4 | 3 | 2300 | 1 | 17 | 5 | 1 | 1.5 |
| 166.5 | 3 | 1600 | 0 | 19 | 3 | 0 | 2.5 |
| 189.4 | 4 | 2200 | 1 | 24 | 1 | 1 | 2 |
| 312.1 | 7 | 2400 | 1 | 13 | 3 | 1 | 3 |
| 289.8 | 6 | 2000 | 1 | 21 | 3 | 1 | 3 |
| 269.9 | 5 | 2200 | 0 | 11 | 4 | 1 | 2.5 |
| 154.3 | 2 | 2000 | 1 | 13 | 2 | 0 | 2 |
| 222.1 | 2 | 2100 | 1 | 9 | 5 | 1 | 2 |
| 209.7 | 5 | 2200 | 0 | 13 | 2 | 1 | 2 |
| 190.9 | 3 | 2200 | 0 | 18 | 3 | 1 | 2 |
| 254.3 | 4 | 2500 | 0 | 15 | 3 | 1 | 2 |
| 207.5 | 3 | 2100 | 0 | 10 | 2 | 0 | 2 |
| 209.7 | 4 | 2200 | 0 | 19 | 2 | 1 | 2 |
| 294 | 2 | 2100 | 1 | 13 | 2 | 1 | 2.5 |
| 176.3 | 2 | 2000 | 0 | 17 | 3 | 0 | 2 |
| 294.3 | 7 | 2400 | 1 | 8 | 4 | 1 | 2 |
| 224 | 3 | 1900 | 0 | 6 | 1 | 1 | 2 |
| 125 | 2 | 1900 | 1 | 18 | 4 | 0 | 1.5 |
| 236.8 | 4 | 2600 | 0 | 17 | 5 | 1 | 2 |
| 164.1 | 4 | 2300 | 1 | 19 | 4 | 0 | 2 |
| 217.8 | 3 | 2500 | 1 | 12 | 3 | 0 | 2 |
| 192.2 | 2 | 2400 | 1 | 16 | 2 | 0 | 2.5 |
| 125.9 | 2 | 2400 | 1 | 28 | 1 | 0 | 1.5 |
| 220.9 | 2 | 2300 | 0 | 12 | 1 | 1 | 2 |
| 294.5 | 6 | 2700 | 1 | 15 | 3 | 1 | 2 |
| 244.6 | 2 | 2300 | 1 | 9 | 2 | 1 | 2.5 |
| 199 | 3 | 2500 | 0 | 18 | 1 | 0 | 1.5 |
| 240 | 4 | 2600 | 1 | 13 | 4 | 1 | 2 |
| 263.2 | 4 | 2300 | 1 | 14 | 3 | 1 | 2 |
| 188.1 | 2 | 1900 | 1 | 8 | 4 | 1 | 1.5 |
| 243.7 | 6 | 2700 | 1 | 7 | 4 | 1 | 2 |
| 221.5 | 4 | 2300 | 1 | 18 | 3 | 1 | 2 |
| 175 | 2 | 2500 | 1 | 11 | 3 | 0 | 2 |
| 253.2 | 3 | 2300 | 1 | 16 | 2 | 1 | 2 |
| 155.4 | 4 | 2400 | 0 | 16 | 3 | 0 | 2 |
| 186.7 | 5 | 2500 | 0 | 21 | 4 | 0 | 2.5 |
| 179 | 3 | 2400 | 0 | 10 | 4 | 1 | 2 |
| 188.3 | 6 | 2100 | 0 | 15 | 4 | 1 | 2 |
| 227.1 | 4 | 2900 | 1 | 8 | 4 | 1 | 2 |
| 173.6 | 4 | 2100 | 0 | 14 | 2 | 1 | 2.5 |
| 188.3 | 5 | 2300 | 1 | 20 | 5 | 0 | 1.5 |
| 310.8 | 8 | 2900 | 1 | 9 | 4 | 1 | 2 |
| 293.7 | 6 | 2400 | 1 | 11 | 5 | 1 | 3 |
| 179 | 3 | 2400 | 1 | 8 | 4 | 1 | 2 |
| 188.3 | 6 | 2100 | 0 | 14 | 2 | 1 | 2.5 |
| 227.1 | 4 | 2900 | 1 | 20 | 5 | 0 | 1.5 |
| 173.6 | 4 | 2100 | 1 | 9 | 4 | 1 | 2 |
| 188.3 | 5 | 2300 | 1 | 11 | 5 | 1 | 3 |
Solution
a) H0: mean selling price = 220 ag. mean selling price > 220...
Population mean = 221.1029...and population s.d = 47.1054...
Test statistic = (221.1029 - 220 ) / (47.1054/ sqrt( 105) ) = 0.23991..
p-value= 0.4054361..
so, we should accept H0 that is mean is 220 , not more than 220..
(b) H0 : mean size = 2100 against H1 :MEan SIZE > 2100
TEST STATISTIC = ( 2223.81 - 2100) / ( 248.6594 / sqrt(105) ) = 5.102039..
p-value = 0.00000077
which is less than 0.1..
so , mean score is greater than 2100...
3) H0 : proportion = 0.6 ag H1 : proportion > 0.60
proportion in the sample = 0.6762...
test statistic = ( 0.6762 - 0.6) / sqrt[ 0.6 * 0.4 / 105 ] = 1.593837...
p-value = 0.05548627..
which is more than 0.05...
so, accept H0 and proportion is 0.6 and not more than that!
d) H0: H0 : proportion = 0.6 ag H1 : proportion > 0.60
test statistic = ( 0.638095 - 0.6) / sqrt[ 0.6 * 0.4 / 105 ] = 0.7968141
P-VALUE = 0.2127795
WHICH IS MORE THAN 0.05.SO ACCEPT H0 and conclude that proportion is not more than 60%...
