Gulf real estate properties sol

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Q.1. Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View
condominiums
ANS: [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
Gulf View condominiums
*List & Sale Prices are in thousands of dollars, Converted to dollars
List Price Sale Price Days to Sell
Mean 474007.5 Mean 454222.5 Mean 106
Standard Error 31194.29258 Standard Error 30439.72954 Standard Error 8.256077792
Median 437000 Median 417500 Median 96
Mode 975000 Mode 305000 Mode 85
Standard
Deviation
197290.0291
Standard
Deviation
192517.7534
Standard
Deviation
52.21602073
Sample
Variance
38923355583
Sample
Variance
37063085378
Sample
Variance
2726.512821
Kurtosis 1.011328907 Kurtosis 1.183621479 Kurtosis 2.02202587
Skewness 1.095814639 Skewness 1.159387914 Skewness 1.077642123
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%)
63096.41236
Confidence
Level (95.0%)
61570.16455
Confidence
Level (95.0%)
16.69949359
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Q.2. Use appropriate descriptive statistics to summarize each of the three variables for the 18 No Gulf
View condominiums
ANS: [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
No Gulf View condominiums
*List & Sale Prices are in thousands of dollars, Converted to dollars

2. List Price Sale Price Days to Sell
Mean 212805.5556 Mean 203188.8889 Mean 135
Standard Error 11536.51342 Standard Error 10345.37846 Standard Error 17.98401614
Median 212500 Median 203500 Median 126
Mode 279000 Mode 179000 Mode -
Standard
Deviation 48945.28124
Standard
Deviation 43891.72358
Standard
Deviation
76.2997186
Sample
Variance 2395640556
Sample
Variance 1926483399
Sample
Variance
5821.647059
Kurtosis -0.08523964 Kurtosis -0.464068271 Kurtosis 2.215301224
Skewness 0.543955061 Skewness 0.30418061 Skewness 1.360546957
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%) 24339.91574
Confidence
Level (95.0%) 21826.84063
Confidence
Level (95.0%)
37.94295741
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Q.3. Compare your summary results. Discuss any specific statistical results that would help a real estate
agent understand the condominium market.
ANS:
Below are the observations and inferences made:
i. Mean of list price and sale price of no gulf view condominiums is smaller than that of the
gulf view condominiums. Whereas the days to sell of the no gulf view condominiums is
greater than that of the gulf view condominiums.
List price mean [474007.5>212805.556]

3. Sale price mean [454222.5>203188.89]
Days to Sell mean [106<135]
ii. Mode in case of the list price and sale price of no gulf view condominiums is smaller than
the gulf view condominiums, whereas the number of days to sell in case of no gulf view
condominiums is not repeated, therefore mode cannot be computed.
List price mode [975000>279000]
Sale price mode [305000>179000]
iii. Median for list price and sale price of no gulf view condominiums are lower than the gulf
view condominiums & the number of days to sell in case of no gulf view condominiums is
greater than the gulf view condominium.
List price median [437000>212500]
Sale price median [417500>203500]
Days to Sell median [96<126]
iv. Standard deviation and the variance is greater for list price and sale price of gulf view
condominium than no gulf view condominium & for the days to sell, the standard deviation
and variance is greater for no gulf view condominiums.
Conclusion:
The Gulf view condominiums are in higher demand then the No Gulf view condominiums as
there list price & Sale price are higher and days to sell is less.
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Q.4. Develop a 95% confidence interval of the population mean sales price and population mean
number of days to sell for Gulf view condominiums. Interpret your results.
ANS: [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
95% Confidence level for the population of mean sale price of Gulf view Condominium
Confidence range MEAN SALE PRICE – 454222.5 ± 61570.16
Range
Mean +95% Conf. Level 515792.6645
Mean -95% Conf. Level 392652.3355
95% interval between the population mean sales is somewhere between (392652.34, 515792.66)
Interpretation –
The confidence interval at 95% is between (392652.34, 515792.66) and it indicates a significance level of
0.05/5%.
95% confidence level for the population of mean days to sell Gulf view Condominium
Confidence range MEAN DAYS TO SELL – 106 ± 16.70
Range
Mean +95% Conf. Level 122.6994936
Mean -95% Conf. Level 89.30050641

4. 95% interval between the population mean sales is somewhere between (89.30, 122.70)
Interpretation –
The confidence interval at 95% is between (89.30, 122.70) which states that the frequency of the
possible confidence intervals that would contain the value of the corresponding parameter.
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Q.5. Develop a 95% confidence interval of the population mean sales price and population mean
number of days to sell for No Gulf view condominiums. Interpret your results.
ANS: [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
95% Confidence level for the population of mean sale price of no gulf view condominium
Confidence range MEAN SALE PRICE - 203188.889±21826.841
Range
Mean +95% Conf. Level 225015.7295
Mean -95% Conf. Level 181362.0483
95% interval between the population mean sales is somewhere between (181362.0483, 225015.7295).
Interpretation –
The confidence interval at 95% is between (181362.0483, 225015.7295) which states that the frequency of
the possible confidence intervals that would contain the value of the corresponding parameter.
95% Confidence level for the population of mean sale price of no gulf view condominium
Confidence range MEAN DAYS TO SELL - 135±37.94
Range
Mean +95% Conf. Level 172.9429574
Mean -95% Conf. Level 97.05704259
95% interval between the population mean sales is somewhere between (97.06, 172.94).
Interpretation –
The confidence interval at 95% is between (97.06, 172.94) which states that the frequency of the
possible confidence intervals that would contain the value of the corresponding parameter.
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Q.6. Assume the branch manager requested estimates of the mean selling price of Gulf view
condominiums with a margin of Error $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 be the sample size.
ANS:

5. 1. Gulf view condominium :
Confidence level: 95%
Confidence coefficient (1-α) = 0.95
α = 1-0.95 = 0.05
Zα/2 = Z0.025 = 1.96 [As per standard normal probability table, an area of α/2 =0.025 in the upper tail provides Z0.025=1.96]
σ = SD of sale price = 192517.7534 [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
Margin of error (E) = $40,000
Sample Size:
Sample size =n= ([(1.96)^2]*[(192517.7534)^2])/(40000)^2 =88.98846798 = 89 (Calculation in attached excel)
2. No Gulf view condominium :
Confidence level: 95%
Confidence coefficient (1-α) = 0.95
α = 1-0.95 = 0.05
Zα/2=Z0.025 =1.96 [As per standard normal probability table, an area of α/2 =0.025 in the upper tail provides Z0.025=1.96]
σ = SD of sale price = 43891.72358 [USING DESCRIPTIVE STATISTICS – DATA ANALYSIS in EXCEL]
Margin of error (E) = $15,000
Sample Size:
Sample size = n = ([(1.96)^2]*[( 43891.72358)^2])/(15000)^2 =32.89235 = 33 (Calculation in attached excel)
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Q.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?
ANS:

6. Gulf view condominium:
List Price Mean = $474007.5
Sale Price Mean= $454222.5
Difference = List Price Mean - Sale Price Mean = 474007.5 – 454222.5 = 19785
= (List Price Mean - Sale Price Mean)/ List Price Mean
=19.785/474007.5 = 0.041739846 = 4.2%
Gulf view condominium sell on average 4.2% below its list price.
Estimating final selling price = (1-0.041739846)*new list price = 0.95826*589,000 = 564421.23 = 564421
Using mean days it is expected to be sold in 106 Days
No Gulf view condominium:
List Price Mean = $ 212805.555555556
Sale Price Mean= $ 203188.888888889
Difference = List Price Mean - Sale Price Mean = 9.61667
= (List Price Mean - Sale Price Mean)/ List Price Mean
=9.61667/212.80556= 0.0451899 = 4.5%
Gulf view condominium sell on average 4.5% below its list price.
Estimating final selling price = (1-0.0451899)*new list price = 0.95481*285,000= 272120.9 = 272121
Using mean days it is expected to be sold in 135 Days
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