Quantitative Studies

Part A

a) Calculation of the sample mean and the sample standard deviation for all three suburbs.

Sample mean

Sample standard deviation

i. Appraised value:

,

Sample mean:

Sample Standard Deviation:

ii. House size

,

Sample mean:

Sample Standard Deviation:

iii. Age

,

Sample mean:

Sample Standard Deviation:

iv. Land Acreage

,

Sample mean:

Sample Standard Deviation:

b) 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.

c) 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).

d) Calculation of skewness in the data set using Pearson's Cofficient of skewness developed.

Address Appraised Value Land (acres) House Size

(sq ft) Age 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:

i. All three suburbs combined

 Appraised Value

 Land (acres)

 House Size (sq ft)

 Age

 Baths

 Garage

ii. Glen Cove

 Land (acres)

 House Size (sq ft)

 Age

 Rooms

iii. Roslyn

 Land (acres)

 House Size (sq ft)

 Age

 Rooms

iv. Freeport

 Land (acres)

 House Size (sq ft)

 Rooms

 Baths garage

The data set of "Appraised Value" for Freeport is the least skewed.

e) 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:

f) Calculation of the confidence intervals

Estimating the confidence interval for the mean:

Estimating the confidence interval for the proportion:

i. 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

95%

With 95% confidence, population mean of "House size" for all suburbs is estimated to be between 1873.8304 and 2016.3696 square feet.

ii. 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