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