Gulf Real Estate PropertiesFernando González

Ricardo Siller

Tania Elizabeth

Santiestéban Treviño

Gulf Real Estate Properties

Gulf Real Estate Properties, Inc., is a real state firm located in Southwest Florida. The company, which advertises itself as “expert in the real state market,” monitors condominium sales by collecting data on location, list price, and number of days it takes to sell each unit.

Each condominium is classified as Gulf View if its located directly on the Gulf of Mexico or No Gulf View if its located on th bay or a golf course, near but not on the Gulf. Sample data from the Multiple Listing Service in Naples, Florida, provided recent sales data for 40 Gulf View Condominiums and 18 No Gulf View condominiums.

Prices are in thousands of dollars. The data are shown in the book page 325.

Descriptive Statistics (Gulf View Condominiums)

List Price: Gulf View

Sample Size 40

Minimum $169,900

Maximum $975,000

Range $805,100

Median $437,000

Mean $474,007.50

St. Dev. $197,290.03

Sales Price: Gulf View

Sample Size 40

Minimum $165,000

Maximum $975,000

Range $810,000

Median $417,500

Mean $454,222.50

St. Dev. $192,517.75

Days to Sell: Gulf View

Sample Size 40

Minimum 28

Maximum 282

Range 254

Median 96

Mean 106.00

St. Dev. 52.22

Descriptive Statistics (No Gulf View Condominiums)

List Price: No Gulf View

Sample Size 18

Minimum $148,000

Maximum $322,000

Range $174,000

Median $212,500

Mean $212,805.56

St. Dev. $48,945.28

Sales Price: No Gulf View

Sample Size 18

Minimum $135,500

Maximum $292,500

Range $157,000

Median $203,500

Mean $203,188.89

St. Dev. $43,891.72

Days to Sell: No Gulf View

Sample Size 18

Minimum 48

Maximum 338

Range 290

Median 126

Mean 135.00

St. Dev. 76.30

Comparison of the Descriptive Statistics (1/2)

List price:

The Gulf View condos have a higher average listing price than No Gulf View Condos ($474,007.50 vs. $212,805.56).

The Gulf View condos also have a higher median listing price than No Gulf View Condos ($437,000 vs. $212,500).

The data for the Gulf View condos are more variable than the data for the No Gulf View condos (larger range and standard deviation).

Comparison of the Descriptive Statistics (2/2)

Sales Price:

The Gulf View condos have a higher average sales price than No Gulf View Condos ($454,222.50 vs. $203,188.89).

The Gulf View condos also have a higher median sales price than No Gulf View Condos ($417,500 vs. $203,500).

The data for the Gulf View condos are more variable than the data for the No Gulf View condos (larger range and standard deviation).

Conclusions: The Gulf View condos seem to be in higher demand than the No Gulf View condos as evidenced by their higher prices and shorter time to sell.

Confidence Interval. Sales Price (Gulf View Condominiums)

Data:

Sample Size (n) 40

Sample Mean (X-bar) 454.2225

Sample Standard Deviation (S)

192.5177

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

39

Z value (0.9750) 1.96

Interval (Large-Sample, s unknown)

Conclusion: With a 95% confidence we can expect that population mean of sales price (gulf view condominium) is within this range

x zsn

/2

Interval

(392.65, 515.79)

Confidence Interval. Days to sell (Gulf View Condominiums)

Data:

Sample Size (n) 40

Sample Mean (X-bar) 106

Sample Standard Deviation (S)

52.2160

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

39

Z value (0.9750) 1.96

Interval (Large-Sample, s unknown)

Conclusion: With a 95% confidence we can expect that population mean of days to sell (gulf view condominium) is within this range

x zsn

/2

Interval

(89.30, 122.70)

Confidence Interval. Sales Price (No Gulf View Condominiums)

Data:

Interval (Small-Sample, s unknown)

Population is normally distributed and s unknown

Conclusion: With a 95% confidence we can expect that population mean of sales price ( no gulf view condominium) is within this range

Sample Size (n) 18

Sample Mean (X-bar) 203.1888

Sample Standard Deviation (S)

43.8917

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

17

T-value (0.025, 17) 2.110

n

stx 2/

Interval

(181.36, 225.02)

Confidence Interval. Days to sell (No Gulf View Condominium)

Data:

Sample Size (n) 18

Sample Mean (X-bar) 135

Sample Standard Deviation (S)

76.2997

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

17

T-value (0.025, 17) 2.110

Interval (Small-Sample, s unknown)

Population is normally distributed and s unknown

Conclusion: With a 95% confidence we can expect that population mean of days to sell ( no gulf view condominium) is within this range.

n

stx 2/

Interval

(97.06, 172.94)

Sample size. Sales Price (Gulf View

Condominiums)

95% confidence level

Margin of error: $40,000. E=40

Sample Size (n) 40

Sample Mean (X-bar) 454.2225

Sample Standard Deviation (S)

192.5177

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

39

Z value(0.975) 1.96

E zn

/2

nz

E( )/ 2

2 2

2

n size

88.98 = 89

Sample size. Sales Price (No Gulf View Condominiums)

95% confidence level

Margin of error: $15,000. E=15

nz

E( )/ 2

2 2

2

Sample Size (n) 18

Sample Mean (X-bar) 203.1888

Sample Standard Deviation (S)

43.8917

Confidence level (%) 95%

Alpha (α) 0.05

Degrees of freedom (n-1)

17

Z value(0.975) 1.96

E zn

/2

n size

32.89 = 33

Estimation New Gulf View Condominium

A Gulf View condominium sells on average 4.2% below its list price.

The estimated selling price is $589,000 x .958 = $564,262. Using the mean days, it is estimated to sell in about 106 days.

Estimation New No Gulf View Condominium

A No Gulf View condominium sells on average 4.5% below its list price.

The estimated selling price is $285,000 x .955 = $272,175. Using the mean days, it is estimated to sell in about 135 days.

And That’s it! Thank you