Case 2: Gulf Real Estate Properties. Please provide a Managerial Report that includes: 1. Appropriate descriptive statistics to summarize each of the three variables for the forty Gulf View condominiums 2. Appropriate descriptive statistics to summarize each of the three variables for the eighteen No-Gulf View condominiums 3. Comparison of your summary results from #1 & #2. Discuss any specific statistical results that would help a real estate agent understand the condominium market. 4. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. 5. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. Also, consider the following scenario and include your responses in your Report: 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 effort of $15,000. Using 95% confidence, how large should the sample sizes be?
GULF VIEW CONDOMINIUMS
List Price Sales Price Days to Sell
495000 475000 130
379000 350000 71
529000 519000 85
552500 534500 95
334900 334900 119
550000 505000 92
169900 165000 197
210000 210000 56
975000 945000 73
314000 314000 126
315000 305000 88
885000 800000 282
975000 975000 100
469000 445000 56
329000 305000 49
365000 330000 48
332000 312000 88
520000 495000 161
425000 405000 149
675000 669000 142
409000 400000 28
649000 649000 29
319000 305000 140
425000 410000 85
359000 340000 107
469000 449000 72
895000 875000 129
439000 430000 160
435000 400000 206
235000 227000 91
638000 618000 100
629000 600000 97
329000 309000 114
595000 555000 45
339000 315000 150
215000 200000 48
395000 375000 135
449000 425000 53
499000 465000 86
439000 428500 158
No Gulf View Condominiums
List Price Sales Price Days to Sell
217000 217000 182
148000 135500 338
186500 179000 122
239000 230000 150
279000 267500 169
215000 214000 58
279000 259000 110
179900 176500 130
149900 144900 149
235000 230000 114
199800 192000 120
210000 195000 61
226000 212000 146
149900146500 137
160000 160000 281
322000 29250063
187500 179000 48
247000 227000 52
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Answers
(1)Descriptive statistics to summarize each of the three variables for the forty Gulf View condominiums
List Price / Sales Price / Days to SellMean / 474007.5 / Mean / 454222.5 / Mean / 106
Standard Error / 31194.293 / Standard Error / 30439.72954 / Standard Error / 8.256078
Median / 437000 / Median / 417500 / Median / 96
Mode / 975000 / Mode / 305000 / Mode / 85
Standard Deviation / 197290.03 / Standard Deviation / 192517.7534 / Standard Deviation / 52.21602
Sample Variance / 3.892E+10 / Sample Variance / 37063085378 / Sample Variance / 2726.513
Kurtosis / 1.0113289 / Kurtosis / 1.183621479 / Kurtosis / 2.022026
Skewness / 1.0958146 / Skewness / 1.159387914 / Skewness / 1.077642
Range / 805100 / Range / 810000 / Range / 254
Minimum / 169900 / Minimum / 165000 / Minimum / 28
Maximum / 975000 / Maximum / 975000 / Maximum / 282
Sum / 18960300 / Sum / 18168900 / Sum / 4240
Count / 40 / Count / 40 / Count / 40
Confidence Level(95.0%) / 63096.412 / Confidence
Level(95.0%) / 61570.16398 / Confidence
Level(95.0%) / 16.69949
(2)Descriptive statistics to summarize each of the three variables for the eighteen No-Gulf View condominiums
List Price / Sales Price / Days to SellMean / 212805.6 / Mean / 203188.9 / Mean / 135
Standard Error / 11536.51 / Standard Error / 10345.38 / Standard Error / 17.98402
Median / 212500 / Median / 203500 / Median / 126
Mode / 279000 / Mode / 179000 / Mode / #N/A
Standard Deviation / 48945.28 / Standard Deviation / 43891.72 / Standard Deviation / 76.29972
Sample Variance / 2.4E+09 / Sample Variance / 1.93E+09 / Sample Variance / 5821.647
Kurtosis / -0.08524 / Kurtosis / -0.46407 / Kurtosis / 2.215301
Skewness / 0.543955 / Skewness / 0.304181 / Skewness / 1.360547
Range / 174000 / Range / 157000 / Range / 290
Minimum / 148000 / Minimum / 135500 / Minimum / 48
Maximum / 322000 / Maximum / 292500 / Maximum / 338
Sum / 3830500 / Sum / 3657400 / Sum / 2430
Count / 18 / Count / 18 / Count / 18
Confidence Level(95.0%) / 24339.92 / Confidence Level(95.0%) / 21826.84 / Confidence Level(95.0%) / 37.94296
(3)Comparisons
The mean sale price of gulf view condominiums is greater than that of non gulf view condominiums.
The mean number of days to sell gulf view condominiums is less tha that of non gulf view condominiums.
The variation in the sale prices of gulf view condominiums are more than that of non gulf view condominiums.
The variation in the number of days to sell of gulf view condominiums are more than that of non gulf view condominiums.
(4)GULF VIEW CONDOMINIUMS
95% confidence interval for population mean sales price is 45422.50±61570.16 =(392652.34,515792.66)
95% confidence interval for population mean days to sell is 106±16.70 =(89.30,122.70)
(5)NON GULF VIEW CONDOMINIUMS
95% confidence interval for population mean sales price is 203188.90±21826.84=(181362.05,225015.73)
95% confidence interval for population mean days to sell is 135±37.94=(97.06,172.94)
(6)GULF VIEW CONDOMINIUMS
Confidence level = 95%
z= 1.96
s=192517.75
E=Z*s/√n = 40000
n = (1.96*192517.75/40000)^2 = 88.99
The minimum sample size is 90
GULF VIEW CONDOMINIUMS
Confidence level = 95%
z= 1.96
s=43891.72
E=Z*s/√n = 15000
n = (1.96*43891.72/15000)^2 = 32.89
The minimum sample size is 33