Gulf Real Estate Properties Gulf Real Estate Properties, Inc., is a real estate firm located in southwest Florida. The company, which advertises itself as “expert in the real estate market,” monitors condominium sales by collecting data on location, list price, sale price, and number of days it takes to sell each unit. Each condominium is classified as Gulf View if it is located directly on the Gulf of Mexico or No Gulf View if it is located on the 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 Table 8.7. Managerial Report 1. Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums. 2. Use appropriate descriptive statistics to summarize each of the three variables for the 18 No Gulf View condominiums. 3. Compare your summary results. Discuss any specific statistical results that would help a real estate agent understand the condominium market. 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. 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. 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? 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?

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The given sample data from the multiple listing Service in Naples, Florida, provided sales data for 40 Gulf View condominiums and 18 No Gulf View condominiums. Prices are in thousands" of dollars.1)Using Minitab we obtain the appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums and the output is as shown below.Descriptive statistics: GV List Price, GV Sale Price, GV DaysThe data contain at least five mode values. Only the ansllest four are show.CommentStep 2 of 11 八The three variables used above are list price, saleprice and number of days.CommentStep 3 of 11 A2)Using Minitab we obtain the appropriate descriptive statistics to summarize each of the three variables for the 18 No- Gulf View condominiums and the output is as shown below.Descriptive statistics: NGV List Price, NGV Sale Price, NGV DaysCommentStep 4 of 11 AThe three variables used above are list price, saleprice and number of days.We comparing the summary results we construct the histograms for each group as follows:Histogram of NGV List Price, NGV Sale Price, NGV Days NormeFrom the above Histograms we compare the summary results in GV list price in the shape of leptokurtotic and it is in NGV list price in the shape of mesokurtotic. Also the GV sale price and GV days in the shape of platykurtotic and it is peaked to leptokurtotic in NGV Condominiums. The statistical results that would help a real estate agent understand the condominium market.CommentStep 6 of 11 人4)Using Minitab to develop a 95 \% Confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. The obtained output is as shown below.One-Sample Z: GV Sale PriceIhe assuned standard deviation =192.5\begin{array}{lrrrrc}\text { Variable } & \text { d } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \text { CI } \\ \text { GV Sale Price } & 40 & 454.2 & 192.5 & 30.4 & (394.6,513.9)\end{array}One-Sample Z: GV DaysThe assumed standard deviation =52.22Variable N Mean StDev sE Mean 95 t \mathrm{CI}GV Days 40 \quad 106.00 \quad 52.22 \quad 8.26 (69.62, 122.18)Using Minitab to 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. The obtained output is as shown below.One-sample Z: NGV sale PriceIhe ansumed standard deviation - 43.9\begin{array}{lrrrrr}\text { Variable } & \text { Mean } & \text { SeDer SE Mear } & 95 \% \text { CI } \\ \text { NGV Sale Price } 18 & 203.2 & 43.9 & 10.3 & \{182.9,223.5\}\end{array}One-5ample Z: NGV DaysIhe ansumed standard deviation - T6.3Variable F Mean StDev SE Mear 95 \% CINפV Days 18 135.0 76.3 \quad 18.0 \quad(99.8,170.2)CommentStep 8 of 118)By the definition of sample size we haven=\left[\frac{Z_{e \cdot 2} \sigma}{E}\right]^{2}From the given information, by using Mega stat we find the sample size selling price of Gulf View condominiums and No Gulf View condominiums the output is as follows:CommentSample size - mean40000 E, error tolerance192.5 standard deviation95 \% confidence level1.960 z0.000 sample size1 rounded upsize - mean15000 E, error tolerance43.9 standard deviation95 \% confidence level1.960 z0.000 sample size1 rounded up40000 E, error tolerance192.5 standard deviation95 \% confidence level1.960 z0.000 sample size1 rounded upSample size - mean15000 E, error tolerance43.9 standard deviation95 \% confidence level1.96020.000 sample size1 rounded upStep 9 of 11 \mathrm{~A}It is given that a gulf view condominium with a list price of \$ 285,000 and a No Gulf View condominium with a list price of \$ 285,000. We need to estimate of the final selling price and number of days required selling each of these units.By using regression analysis to predict the final selling price and number of days required selling each of these units as follows.Let x denote the list price which is an independent variable and y denote selling price, which is dependent variable.Regression Analysis: GV Sale Price versus GV List PriceThe regresaion equation isGV Sale Price =-6.98+0.979 GV List PriceThe estimated prediction of the final selling price is 573.0(\$ 1000).CommentStep 11 of 11Regression Analysis: NGV Sale Price versus NGV List PriceThe regression equation isNGV Sale Price =14.0+0.889 NGV List Price\begin{array}{lrrrr}\text { Predietot } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 13.989 & 6.384 & 2.19 & 0.041 \\ \text { NGV List Price } & 0.88907 & 0.02927 & 30.37 & 0.000\end{array}3=5.90782 \quad \mathrm{R}-S \mathrm{q}=98.3 q \quad \mathrm{R}-\mathrm{q}[\mathrm{adj}]=98.2 zMnalyais of Variance\begin{array}{lrrrrr}\text { Source } & \text { DE } & 93 & \text { MS } & \text { F } & \text { P } \\ \text { Reyression } & 1 & 92192 & 32192 & 922.31 & 0.000 \\ \text { Regidual Error } & 16 & 558 & 35 & & \\ \text { Total } & 17 & 92750 & & & \end{array}Predicted Values for Bew ObservationsNew obs FLE SE FLE NiE CI 95 z \mathrm{CI}1259399.67 \quad 8337.05 \quad(235725.92,271073.13) \quad(235725.91,271073.43) x XXx denotes a point that is an extrexe outliet in the predictors.Values of Predietors for lew ObeervationeNew obs Iist PriceThe estimated prediction of the final selling price is 253.33(\$ 1000). ...