gulf view case
TRANSCRIPT
Gulf View Condominiums
1 495 475 130379 350 71529 519 85
552.5 534.5 95334.9 334.9 119550 505 92
169.9 165 197210 210 56975 945 73314 314 126315 305 88885 800 282975 975 100469 445 56329 305 49365 330 48332 312 88520 495 161425 405 149675 669 142409 400 28649 649 29319 305 140425 410 85359 340 107469 449 72895 875 129439 430 160435 400 206235 227 91638 618 100629 600 97329 309 114595 555 45339 315 150215 200 48395 375 135449 425 53
1. Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums.
List Price
Sale Price
Days to Sell
499 465 86439 428.5 158
list price
Mean 473.4692Standard Error 31.9999Median 435Mode 975Standard Deviation 199.8393Sample Variance 39935.76Kurtosis 0.927667Skewness 1.092105Range 805.1Minimum 169.9Maximum 975Sum 18465.3Count 39
sale price
Mean 453.6897Standard Error 31.22572Median 410Mode 305Standard Deviation 195.0046Sample Variance 38026.78Kurtosis 1.09735Skewness 1.155106Range 810Minimum 165Maximum 975Sum 17693.9Count 39
days to sell
Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums.
Mean 105.3846Standard Error 8.446994Median 95Mode 85Standard Deviation 52.75146Sample Variance 2782.717Kurtosis 2.013884Skewness 1.108391Range 254Minimum 28Maximum 282Sum 4110Count 39
217 217 182148 135.5 338
186.5 179 122239 230 150279 267.5 169215 214 58279 259 110
179.9 176.5 130149.9 144.9 149235 230 114
199.8 192 120210 195 61226 212 146
149.9 146.5 137160 160 281322 292.5 63
187.5 179 48247 227 52
2. Use appropriate descriptive statistics to summarize each of the three variables for the 18 NO Gulf View condominiums.
No Gulf View CondominiumsList
PriceSale Price
Days to Sell
list price
Mean 212.5588Standard Error 12.23352Median 210Mode 279Standard Deviation 50.4401Sample Variance 2544.204Kurtosis -0.245792Skewness 0.548579Range 174Minimum 148Maximum 322Sum 3613.5Count 17
sale price
Mean 202.3765Standard Error 10.93904Median 195Mode 179Standard Deviation 45.10283Sample Variance 2034.266Kurtosis -0.559708Skewness 0.359272Range 157Minimum 135.5Maximum 292.5Sum 3440.4Count 17
days to sell
Mean 132.2353Standard Error 18.84818Median 122
Use appropriate descriptive statistics to summarize each of the three variables for the 18 NO Gulf View condominiums.
Mode #N/AStandard Deviation 77.71304Sample Variance 6039.316Kurtosis 2.474568Skewness 1.483614Range 290Minimum 48Maximum 338Sum 2248Count 17
LIST PRICE COMPARISIONParameter GULF NO GULFMean 473.4692 212.5588Standard Error 31.9999 12.23352Median 435 210Mode 975 279Standard Deviation 199.8393 50.4401Sample Variance 39935.76 2544.204Kurtosis 0.927667 -0.245792Skewness 1.092105 0.548579Range 805.1 174Minimum 169.9 148Maximum 975 322Sum 18465.3 3613.5Count 39 17
SALE PRICE COMPARISIONParameter GULF NO GULFMean 453.6897 202.3765Standard Error 31.22572 10.93904Median 410 195Mode 305 179Standard Deviation 195.0046 45.10283Sample Variance 38026.78 2034.266Kurtosis 1.09735 -0.559708Skewness 1.155106 0.359272Range 810 157Minimum 165 135.5Maximum 975 292.5Sum 17693.9 3440.4Count 39 17
DAYS TO SELL COMPARISIONParameter GULF NO GULFMean 105.3846 132.2353Standard Error 8.446994 18.84818Median 95 122Mode 85 #N/AStandard Deviation 52.75146 77.71304
3. Compare your summary results. Discuss any specific statistical results that would help a real estate agent understand the condominium market.
1 20
50
100
150
200
250
300
350
400
450
500
Mean
Mean
Mean
1 20
50
100
150
200
250
Standard Deviation
Standard Deviation
Standard Deviation
Sample Variance 2782.717 6039.316Kurtosis 2.013884 2.474568Skewness 1.108391 1.483614Range 254 290Minimum 28 48Maximum 282 338Sum 4110 2248Count 39 17
1 20
50
100
150
200
250
Standard Deviation
Standard Deviation
Standard Deviation
Compare your summary results. Discuss any specific statistical results that would help a real estate agent understand the condominium market.
1 20
50
100
150
200
250
300
350
400
450
500
Mean
Mean
Mean
1 20
50
100
150
200
250
Standard Deviation
Standard Deviation
Standard Deviation
1 20
50
100
150
200
250
Standard Deviation
Standard Deviation
Standard Deviation
Compare your summary results. Discuss any specific statistical results that would help a real estate agent understand the condominium market.
SALE PRICE AT 95% CONFIDENCE INTERVAL DAYS TO SELL AT 95% CONFIDENCE INTERVALX X-X (X-X)^2
sale price 475 21.3103 454.1289Mean 453.6897 350 -103.6897 10751.55
519 65.3103 4265.435
534.5 80.8103 6530.305days to sell 334.9 -118.7897 14110.99
Mean 105.3846 505 51.3103 2632.747
165 -288.6897 83341.74
210 -243.6897 59384.67
945 491.3103 241385.8
314 -139.6897 19513.21
305 -148.6897 22108.63
800 346.3103 119930.8
975 521.3103 271764.4
445 -8.6897 75.51089
305 -148.6897 22108.63
330 -123.6897 15299.14
312 -141.6897 20075.97
495 41.3103 1706.541
405 -48.6897 2370.687
669 215.3103 46358.53
400 -53.6897 2882.584
649 195.3103 38146.11
305 -148.6897 22108.63
410 -43.6897 1908.79
340 -113.6897 12925.35
449 -4.6897 21.99329
875 421.3103 177502.4
430 -23.6897 561.2019
400 -53.6897 2882.584
227 -226.6897 51388.22
618 164.3103 26997.87
600 146.3103 21406.7
309 -144.6897 20935.11
555 101.3103 10263.78
315 -138.6897 19234.83
200 -253.6897 64358.46
375 -78.6897 6192.069
425 -28.6897 823.0989
465 11.3103 127.9229
428.5 -25.1897 634.521
4. Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Interpret your results
∑ 1445472192.5185
76.35346831.026
σn
Lower limit = M - Z.95σn
Upper limit = M + Z.95σn
DAYS TO SELL AT 95% CONFIDENCE INTERVALX X-X (X-X)^2
130 24.6154 605.9179
71 -34.3846 1182.301
85 -20.3846 415.5319
95 -10.3846 107.8399
119 13.6154 185.3791
92 -13.3846 179.1475
197 91.6154 8393.382
56 -49.3846 2438.839
73 -32.3846 1048.762
126 20.6154 424.9947
88 -17.3846 302.2243
282 176.6154 31193
100 -5.3846 28.99392
56 -49.3846 2438.839
49 -56.3846 3179.223
48 -57.3846 3292.992
88 -17.3846 302.2243
161 55.6154 3093.073
149 43.6154 1902.303
142 36.6154 1340.688
28 -77.3846 5988.376
29 -76.3846 5834.607
140 34.6154 1198.226
85 -20.3846 415.5319
107 1.6154 2.609517
72 -33.3846 1114.532
129 23.6154 557.6871
160 54.6154 2982.842
206 100.6154 10123.46
91 -14.3846 206.9167
100 -5.3846 28.99392
97 -8.3846 70.30152
114 8.6154 74.22512
45 -60.3846 3646.3
150 44.6154 1990.534
48 -57.3846 3292.992
135 29.6154 877.0719
53 -52.3846 2744.146
86 -19.3846 375.7627
158 52.6154 2768.38
Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Interpret your results
∑ 106349.152.21974
3.033925207.7353
σn
Lower limit = M - Z.95σn
Upper limit = M + Z.95σn
Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Interpret your results
SALE PRICE AT 95% CONFIDENCE INTERVALX X-X (X-X)^2
sale price 217 14.6235 213.8468Mean 202.3765 135.5 -66.8765 4472.466
179 -23.3765 546.4608
230 27.6235 763.0578days to sell 267.5 65.1235 4241.07
Mean 132.2353 214 11.6235 135.1058
259 56.6235 3206.221
176.5 -25.8765 669.5933
144.9 -57.4765 3303.548
230 27.6235 763.0578
192 -10.3765 107.6718
195 -7.3765 54.41275
212 9.6235 92.61175
146.5 -55.8765 3122.183
160 -42.3765 1795.768
292.5 90.1235 8122.245
179 -23.3765 546.4608
227 24.6235 606.3168∑ 32762.1
43.89968
Lower limit = M - Z.95σn 116.3331Upper limit = M + Z.95σn 288.4198
5. Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for No Gulf View condominiums. Interpret your results
σn
DAYS TO SELL AT 95% CONFIDENCE INTERVALX X-X (X-X)^2
182 49.7647 2476.525
338 205.7647 42339.11
122 -10.2353 104.7614
150 17.7647 315.5846
169 36.7647 1351.643
58 -74.2353 5510.88
110 -22.2353 494.4086
130 -2.2353 4.996566
149 16.7647 281.0552
114 -18.2353 332.5262
120 -12.2353 149.7026
61 -71.2353 5074.468
146 13.7647 189.467
137 4.7647 22.70237
281 148.7647 22130.94
63 -69.2353 4793.527
48 -84.2353 7095.586
52 -80.2353 6437.703∑ 99105.58
76.35274
Lower limit = M - Z.95σn -17.41607Upper limit = M + Z.95σn 281.8867
Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for No Gulf View condominiums. Interpret your results
σn
Develop a 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for No Gulf View condominiums. Interpret your results
6. Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how large should the sample sizes be?
MARGIN OF ERROR = Critical value x Standard error
standard error=standard deviation/sqrt(n)
SQRT(n)=(M/Z*S.E)
α = 1 - (confidence level / 100) = 1 - 0.95 = 0.05
the critical probability (p*): p* = 1 - α/2 = 1 - 0.05/2 = 0.975
Z=1.96
M=40
195.0046
SQRT(n) 9.55522336034306n 91.302293
The sample size needs to be increased by 91 samples for the margin of error of 40000
MARGIN OF ERROR = Critical value x Standard error
standard error=standard deviation/sqrt(n)
SQRT(n)=(M/Z*S.E)
α = 1 - (confidence level / 100) = 1 - 0.95 = 0.05
the critical probability (p*): p* = 1 - α/2 = 1 - 0.05/2 = 0.975
Z=1.96
M=15
45.10283SQRT(n) 5.89343701501379n 34.7326
The sample size needs to be increased by 35 samples for the margin of error of 15000
Standard Deviation
Standard Deviation
6. Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No Gulf View condominiums with a margin of error of $15,000. Using 95% confidence, how large should the sample sizes be?
the critical probability (p*): p* = 1 - α/2 = 1 - 0.05/2 = 0.975
The sample size needs to be increased by 91 samples for the margin of error of 40000
the critical probability (p*): p* = 1 - α/2 = 1 - 0.05/2 = 0.975
The sample size needs to be increased by 35 samples for the margin of error of 15000
7. Gulf Real Estate Properties just signed contracts for two new listings: a Gulf View condominium with a list price of $589,000 and a No Gulf View condominium with a list price of $285,000. What is your estimate of the final selling price and number of days required to sell each of these units?
Correlation between list price and sale price in gulf viewcorrelation between list price and days to sell in gulf view
Gulf View Condominiums
495 475 130
379 350 71 589 587.3005 75.85088529 519 85
552.5 534.5 95334.9 334.9 119550 505 92
169.9 165 197210 210 56975 945 73314 314 126315 305 88885 800 282975 975 100469 445 56329 305 49365 330 48332 312 88520 495 161425 405 149675 669 142409 400 28649 649 29319 305 140425 410 85359 340 107469 449 72895 875 129439 430 160435 400 206235 227 91638 618 100
List Price
Sale Price
Days to Sell
List Price
Sale Price
estimate
Days to Sell estimate
629 600 97329 309 114595 555 45339 315 150215 200 48395 375 135449 425 53499 465 86439 428.5 158
7. Gulf Real Estate Properties just signed contracts for two new listings: a Gulf View condominium with a list price of $589,000 and a No Gulf View condominium with a list price of $285,000. What is your estimate of the final selling price and number of days required to sell each of these units?
0.997115 Correlation between list price and sale price in no gulf view0.128779 correlation between list price and days to sell in no gulf view
217 217 182
148 135.5 338 285 282.5597186.5 179 122239 230 150279 267.5 169215 214 58279 259 110
179.9 176.5 130149.9 144.9 149235 230 114
199.8 192 120210 195 61226 212 146
149.9 146.5 137160 160 281322 292.5 63
187.5 179 48247 227 52
No Gulf View CondominiumsList
PriceSale Price
Days to Sell
List Price
Sale Price
estimate
0.991438-0.453089
129.1303
Days to Sell estimate