Competency
In this project, you will demonstrate your mastery of the following competency:
Apply statistical techniques to address research problems
Perform hypothesis testing to address an authentic problem
Overview
In this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.
Scenario
You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:
Are housing prices in your regional market lower than the national market average?
Is the square footage for homes in your region different than the average square footage for homes in the national market?
For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?
You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.
Directions
Introduction
Region: Start by picking one region from the following list of regions:West South Central, West North Central, East South Central, East North Central, Mid Atlantic
Purpose: What is the purpose of your analysis?
Sample: Define your sample. Take a random sample of 500 house sales for your region.
Describe what is included in your sample (i.e., states, region, years or months).
Questions and type of test: For your selected sample, define two hypothesis questions (see the Scenario above) and the appropriate type of test for each. Address the following for each hypothesis:
Describe the population parameter for the variable you are analyzing.
Describe your hypothesis in your own words.
Identify the hypothesis test you will use (1-Tail or 2-Tail).
Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem.
1-Tail Test
Hypothesis: Define your hypothesis.
Define the population parameter.
Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.
Specify your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:=QUARTILE(, )
Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric.
Check the conditions.
Determine if the normal condition has been met.
Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.
Calculate the probability (p value). Note: This calculation is done with the T.DIST function in Excel:=T.DIST(, , True) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
Relate the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
2-Tail Test
Hypotheses: Define your hypothesis.
Define the population parameter.
Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.
State your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:=QUARTILE(, )
Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note: For shape, think about the distribution: skewed or symmetric.
Check the assumptions.
Determine if the normal condition has been met.
Determine if there are any other conditions that should be checked on and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.]
Determine the probability (p value). Note: This calculation is done with the TDIST.2T function in Excel:=T.DIST.2T(, ) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
Compare the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
Comparison of the test results: Revisit Question 3 from the Scenario section: For your region, what is the range of values for the 95% confidence interval of square footage for homes?
Calculate and report the 95% confidence interval. Show or describe your method of calculation.
Final Conclusions
Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language.
Discuss: Discuss whether you were surprised by the findings. Why or why not?
You can use the following tutorial that is specifically about this assignment:
What to Submit
To complete this project, you must submit the following:
Project Two Template Word Document Use this template to structure your report, and submit the finished version as a Word document. (attachment: template)
Supporting Materials
The following resources may help support your work on the project:
Data Set: MAT 240 House Listing Price by Region SpreadsheetUse this data for input in your project report. (attachment House listing)
Document: National Summary Statistics and Graphs House Listing Price by Region PDFUse this data for input in your project report.
link: https://learn.snhu.edu/content/enforced/1261476-MAT-240-J4761-OL-TRAD-UG.23EW4/course_documents/National%20Summary%20Statistics%20and%20Graphs%20House%20Listing%20Price%20by%20Region.pdf?_&d2lSessionVal=VSwenxR7YPygxkB3gqtRHkFmP&ou=1261476
Regional vs. National Housing Price Comparison Report 2
Report: Regional vs. National Housing Price Comparison
Regional vs. National Housing Price Comparison Report 1
Southern New Hampshire University
Introduction
Region:
Purpose:
Sample:
Questions and type of test:
Level of confidence:
1-Tail Test
Hypothesis:
Hypothesis:
Hypothesis:
Data analysis:
Data analysis:
=QUARTILE(, )
Data analysis:
Data analysis:
Hypothesis Test Calculations:
Hypothesis Test Calculations: , , True).
The degree of freedom is calculated by subtracting 1 from your sample size.]
Interpretation:
Interpretation:
Interpretation:
2-Tail Test
Hypotheses:
Hypotheses:
Hypotheses:
Data Analysis:
Data Analysis: , ) ]
Data Analysis:
Data Analysis:
Hypothesis Test Calculations:
Hypothesis Test Calculations: , ). The degree of freedom is calculated by subtracting 1 from your sample size.]
Interpretation:
Interpretation:
Interpretation:
Comparison of the Test Results:
Final Conclusions
Summarize Your Findings:
Discuss:
,
New England
House Listing Price Data by Region
Source:
https://www.realtor.com/research/data/
Regional sample (n = 1001)
State
County
Region
House listing price
Cost per square foot
Square footage
CT
litchfield
New England
$329,050
$153
1,888
ME
penobscot
New England
$169,500
$103
1,586
NH
merrimack
New England
$299,950
$145
2,152
VT
washington
New England
$289,950
$141
1,959
ME
york
New England
$391,550
$230
1,719
VT
washington
New England
$222,500
$135
1,670
NH
strafford
New England
$311,471
$166
1,885
MA
suffolk
New England
$699,050
$647
1,259
MA
norfolk
New England
$642,500
$309
2,210
NH
hillsborough
New England
$339,950
$164
2,090
RI
washington
New England
$499,050
$259
1,871
NH
belknap
New England
$289,950
$156
1,869
VT
rutland
New England
$228,800
$117
1,993
RI
newport
New England
$579,050
$292
2,128
MA
franklin
New England
$230,050
$133
1,800
ME
penobscot
New England
$157,050
$94
1,600
VT
washington
New England
$300,050
$154
1,896
MA
berkshire
New England
$379,950
$185
2,032
ME
kennebec
New England
$187,050
$104
1,695
NH
cheshire
New England
$266,550
$132
1,981
VT
franklin
New England
$219,950
$120
1,750
CT
new london
New England
$290,000
$153
1,848
NH
merrimack
New England
$314,950
$146
2,174
NH
merrimack
New England
$299,950
$140
2,176
NH
hillsborough
New England
$358,950
$173
2,036
CT
windham
New England
$204,000
$123
1,615
VT
washington
New England
$295,050
$147
1,888
CT
new london
New England
$268,500
$159
1,648
CT
new haven
New England
$279,950
$158
1,724
MA
plymouth
New England
$491,550
$244
2,028
MA
franklin
New England
$223,800
$135
1,780
NH
cheshire
New England
$260,500
$131
1,838
CT
new haven
New England
$279,050
$153
1,790
ME
penobscot
New England
$159,750
$100
1,588
NH
grafton
New England
$259,300
$150
1,840
VT
washington
New England
$299,050
$147
1,850
ME
york
New England
$339,050
$205
1,772
CT
new haven
New England
$272,421
$150
1,763
MA
suffolk
New England
$764,050
$669
1,341
NH
grafton
New England
$253,850
$143
1,741
RI
newport
New England
$598,050
$292
2,170
MA
middlesex
New England
$655,000
$276
2,400
MA
franklin
New England
$299,050
$150
1,960
CT
new london
New England
$274,950
$121
1,212
RI
providence
New England
$279,050
$185
1,504
MA
barnstable
New England
$599,950
$318
1,920
CT
litchfield
New England
$398,050
$172
2,268
NH
belknap
New England
$295,000
$162
1,838
NH
belknap
New England
$269,950
$153
1,797
MA
suffolk
New England
$799,050
$708
1,311
RI
kent
New England
$275,050
$177
1,524
CT
new haven
New England
$258,500
$146
1,410
VT
windsor
New England
$349,050
$158
2,120
CT
litchfield
New England
$329,950
$150
1,776
NH
cheshire
New England
$234,550
$123
1,845
NH
cheshire
New England
$258,864
$126
1,968
NH
hillsborough
New England
$341,444
$160
2,126
RI
washington
New England
$489,950
$253
1,812
CT
middlesex
New England
$342,450
$170
1,874
CT
new london
New England
$294,050
$154
1,880
NH
strafford
New England
$284,950
$155
1,819
MA
suffolk
New England
$774,500
$670
1,359
MA
bristol
New England
$385,050
$210
1,873
MA
bristol
New England
$375,050
$206
1,880
RI
kent
New England
$319,950
$204
1,537
MA
suffolk
New England
$722,500
$645
1,275
MA
hampden
New England
$239,950
$145
1,668
ME
kennebec
New England
$182,050
$108
1,678
MA
suffolk
New England
$882,550
$760
1,385
VT
chittenden
New England
$397,500
$180
2,162
CT
hartford
New England
$263,707
$142
1,850
VT
washington
New England
$279,050
$152
1,752
NH
strafford
New England
$297,550
$149
1,852
CT
hartford
New England
$247,750
$135
1,452
MA
bristol
New England
$399,500
$215
1,847
CT
new london
New England
$317,050
$164
1,884
MA
norfolk
New England
$624,950
$284
2,303
RI
bristol
New England
$499,950
$250
2,234
NH
rockingham
New England
$410,050
$190
2,170
<td
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