Quantitative Studies
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Part A
Calculation of the sample mean and the sample standard deviation for all three suburbs.
Sample mean
Sample standard deviation
Appraised value:
Sample mean:
Sample Standard Deviation:
House size
Sample mean:
Sample Standard Deviation:
Sample mean:
Sample Standard Deviation:
Land Acreage
Sample mean:
Sample Standard Deviation:
The provided data set contains variables in nature, “Address” and “Location” are the categorical random variables. The data is measured on a nominal scale.
Variables such as “Appraised Value”, “Land (acres)”, “House Size (sq ft)”, “Age”, “Rooms”, “Baths” and “Garage” are numerical.
Calculation of the Descriptive statistics for all three suburbs combined and individually using the DATA ANALYSIS tool pack in Excel.
All four printouts for all three suburbs combined and individually (Glencove, Roslyn and Freeport) are in Part (B).
Calculation of skewness in the data set using Pearsons Cofficient of skewness developed.
Address
Appraised Value
Land (acres)
House Size
(sq ft)
Rooms
Baths
Garage
All three suburbs combined
0.77187496
1.044706061
0.41141718
0.645686
-0.08768
0.02185924
-1.5351926
Glen Cove
-0.153134604
0.488326089
0.799105928
0.050676
0.351913
-0.4592779
-0.7000994
Roslyn
-0.153134604
0.488326089
0.799105928
0.050676
0.351913
-0.4592779
-0.7000994
Freeport
-0.012370076
0.92527933
0.880147365
-0.08084
1.434755
0.61007449
1.9309493
The data sets with positive skewness:
All three suburbs combined
Appraised Value
Land (acres)
House Size (sq ft)
Baths
Garage
Glen Cove
Land (acres)
House Size (sq ft)
Rooms
Roslyn
Land (acres)
House Size (sq ft)
Rooms
Freeport
Land (acres)
House Size (sq ft)
Rooms
Baths garage
The data set of “Appraised Value” for Freeport is the least skewed.
Calculation of the sample proportion and its standard deviation for Glencove “Appraisals” whose value ($) is less than 300.
Solutions essential:
Glencove sample size:
Number of “Appraisals whose value ($) is less than 300:
Sample Proportion:
Standard error of the sample proportion:
Calculation of the confidence intervals
Estimating the confidence interval for the mean:
Estimating the confidence interval for the proportion:
A 95% confidence interval for the true population mean “House size” for all suburbs combined.
Solutions essentials:
Using sampling distribution decision tree for the mean normal CLT Z is chosen (the population is not normal, is unknown and ).
Under the significance level ,
That means that a level of confidence 95% leads to a Z value of .
-1.96
0 +1.96 Scale of Z
With 95% confidence, population mean of “House size” for all suburbs is estimated to be between 1873.8304 and 2016.3696 square feet.
A 99% confidence interval for the true population mean “Age” of the home for all suburbs combined.
Solution essentials:
Using sampling distribution decision tree for the mean normal CLT Z is chosen (the population is not normal, is unknown and ).
Under the significance level , .
That means that a level of confidence