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Project Two Guidelines and Rubric.html
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 higher 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
Purpose: What was the purpose of your analysis, and what is your approach?
Define a random sample and two hypotheses (means) to analyze.
Sample: Define your sample. Take a random sample of 100 observations 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 and the appropriate type of test hypothesis 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.
Describe the inference test you will use.
Identify the test statistic.
Level of confidence: Discuss how you will use estimation and conference intervals to help you solve the problem.
1-Tailed Test
Hypothesis: Define your hypothesis.
Define the population parameter.
Write null (Ho) and alternative (Ha) hypotheses.
Specify your significance level.
Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.
Summarize your sample data using appropriate graphical displays and summary statistics.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation.
Summarize your sample data, describing the center, spread, and shape in comparison to the national information.
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.
Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t).
Calculate the probability (p value).
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-Tailed Test
Hypotheses: Define your hypothesis.
Define the population parameter.
Write null and alternative hypotheses.
State your significance level.
Data analysis: Analyze the data and confirm assumptions have not been violated to complete this hypothesis test.
Summarize your sample data using appropriate graphical displays and summary statistics.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation.
Summarize your sample data, describing the center, spread, and shape in comparison to the national information.
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.
Hypothesis test calculations: Complete hypothesis test calculations, providing the appropriate statistics and graphs.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t).
Determine the probability (p value).
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.
Comparison of the test results: See Question 3 from the Scenario section.
Calculate a 95% confidence interval. Show or describe your method of calculation.
Interpret a 95% confidence interval.
Final Conclusions
Summarize your findings: Refer back to the Introduction section above and summarize your findings of the sample you selected.
Discuss: Discuss whether you were surprised by the findings. Why or why not?
What to Submit
To complete this project, you must submit the following:
Project Two Template: Use this template to structure your report, and submit the finished version as a Word document.
Supporting Materials
The following resources may help support your work on the project:
Data Set: House Listing Price by Region
Use this data for input in your project report.
Document: National Statistics and Graphs
Use this data for input in your project report.
Use these tutorials for support with the Excel functions you will use in the project:
Tutorial: Random Sampling in Excel
Tutorial: Scatterplots in Excel
Tutorial: Descriptive Statistics in Excel
Tutorial: Creating Histograms in Excel
Project Two Rubric
Criteria Exemplary Proficient Needs Improvement Not Evident Value
Introduction: Purpose Exceeds proficiency in an exceptionally clear manner (100%) Defines a random sample and two hypotheses to analyze, and provides a brief overview of the report (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing or inaccurate samples or hypotheses (55%) Does not attempt criterion (0%) 5
Introduction: Sample N/A Describes what is included in the defined random sample (i.e., states, regions, or the period of time used) (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or very limited descriptions of what is included in the random sample (55%) Does not attempt criterion (0%) 5
Introduction: Questions and Type of Test Exceeds proficiency in an exceptionally clear and insightful manner (100%) Defines two hypothesis questions and the appropriate type of test hypothesis for each for the defined random samples, addressing the population parameters for the variables, a description of the created hypotheses in their own words, and a description of the inference test to be used (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing or inaccurate descriptions, definitions, or questions (55%) Does not attempt criterion (0%) 5
Introduction: Level of Confidence Exceeds proficiency in an exceptionally clear, insightful, or sophisticated manner (100%) Discusses how estimation and conference intervals will be used to help solve the problem (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing or inaccurate examples of how estimation and conference intervals will be used to help solve the problem (55%) Does not attempt criterion (0%) 10
1-Tailed Test: Hypothesis N/A Defines the hypothesis by defining the population parameter, writing null and alternative hypotheses, and specifying the significance level (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing or inaccurate definitions and specifications (55%) Does not attempt criterion (0%) 5
1-Tailed Test: Data Analysis Exceeds proficiency in an exceptionally clear, insightful, or sophisticated manner (100%) Analyzes the data to confirm that assumptions have not been violated to complete the hypothesis test, summarizes sample data using appropriate graphical displays and summary statistics, and checks the conditions (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or insufficient analyses, summaries, or condition checks (55%) Does not attempt criterion (0%) 5
1-Tailed Test: Complete Hypothesis Test Calculations N/A Completes the hypothesis test calculation and provides appropriate statistics and graphs (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or inappropriate calculations, statistics, and/or graphs (55%) Does not attempt criterion (0%) 5
1-Tailed Test: Interpretation Exceeds proficiency in an exceptionally clear, insightful manner (100%) Interprets hypothesis test results using the p value method to reject or not reject the null hypothesis by relating the p value and significance level, making the correct decision to reject or fail to reject, and providing a contextualized conclusion (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or insufficient interpretations or conclusions (55%) Does not attempt criterion (0%) 5
2-Tailed Test: Hypotheses N/A Defines the hypothesis by defining the population parameter, writing null and alternative hypotheses, and stating the significance level (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing or inaccurate definitions and specifications (55%) Does not attempt criterion (0%) 5
2-Tailed Test: Data Analysis Exceeds proficiency in an exceptionally clear, insightful, or sophisticated manner (100%) Analyzes the data and confirms assumptions have not been violated to complete the hypothesis test by summarizing sample data using appropriate graphical displays and summary statistics and checking the assumptions (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or insufficient analysis, summaries, or condition checks (55%) Does not attempt criterion (0%) 5
2-Tailed Test: Hypothesis Test Calculations N/A Completes the hypothesis test calculation by providing the appropriate statistics and graphs (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or inappropriate calculations, statistics, and/or graphs (55%) Does not attempt criterion (0%) 5
2-Tailed Test: Interpretation Exceeds proficiency in an exceptionally clear, insightful manner (100%) Interprets hypothesis test results using the p value method to reject or not reject the null hypothesis by relating the p value and significance level, making the correct decision to reject or fail to reject, and providing a contextualized conclusion (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or insufficient interpretations or conclusions (55%) Does not attempt criterion (0%) 10
2-Tailed Test: Comparison of the Test Results N/A Calculates and interprets a 95% confidence interval (100%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate calculations or interpretations (55%) Does not attempt criterion (0%) 5
Final Conclusions: Summarize Your Findings Exceeds proficiency in an exceptionally clear, insightful, sophisticated manner (100%) Summarizes findings of selected sample through the context of Step One (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include inaccurate or insufficient interpretations and/or conclusions (55%) Does not attempt criterion (0%) 10
Final Conclusions: Discuss Exceeds proficiency in an exceptionally clear, insightful, or sophisticated, manner (100%) Discusses whether the findings were surprising and why (85%) Shows progress toward proficiency, but with errors or omissions; areas for improvement may include providing more details and evidence to support the response (55%) Does not attempt criterion (0%) 10
Articulation of Response Exceeds proficiency in an exceptionally clear, insightful, sophisticated, or creative manner (100%) Clearly conveys meaning with correct grammar, sentence structure, and spelling, demonstrating an understanding of audience and purpose (85%) Shows progress toward proficiency, but with errors in grammar, sentence structure, and spelling, negatively impacting readability (55%) Submission has critical errors in grammar, sentence structure, and spelling, preventing understanding of ideas (0%) 5
Total: 100%
course_documents/MAT 240 Project Two Template.docx
Regional vs. National Housing Price Comparison Report 2
[Note: To complete this template, replace the bracketed text with your own content. Remove this note before you submit your outline.]
Report: Regional vs. National Housing Price Comparison
[Your Name]
Regional vs. National Housing Price Comparison Report 1
Southern New Hampshire University
Introduction
Purpose: [Include in this section a brief overview, the purpose of the report, and your approach. Define your random sample and two hypotheses (means) to analyze.]
Sample: [Take a random sample of observations from your region and 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 and the appropriate type of test hypothesis for each. For each hypothesis question, answer questions 3a-c from the Project Two Guidelines and Rubric. This includes questions about the population parameter, your hypothesis, the inference method you will use, and how you will use estimation and confidence intervals to help you solve the problem.]
1-Tail Test
Hypothesis: [Define the population parameter. Write null and alternative hypotheses. Note: For means, define a hypothesis that is greater than the population parameter. Specify your significance level.]
Data analysis: [Summarize your sample data using appropriate graphical displays and summary statistics.]
[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([data range], [quartile number])
[Summarize your sample data, describing the center, spread, and shape in context.]
[Note: For shape, think about the distribution: skewed or symmetric.]
[Check the assumptions by determining 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:
[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.RT function in Excel: =T.DIST.RT([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.]
Interpretation:
[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 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.]
[Provide at least one histogram of your sample data.]
[In a table, provide summary statistics including sample size, mean, and standard deviation.]
[Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number]) ]
[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 by determining 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:
[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 TDIST.2T function in Excel: =T.DIST.RT([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.]
Interpretation:
[Relate the p value and significance level.]
[Make the correct decision (reject or fail to reject).]
[Provide a conclusion in context to your hypothesis.]
Comparison of the Test Results:
[Calculate the 95% confidence interval and show or describe the method of calculation.]
[Interpret the confidence 95% confidence interval in context.]
Final Conclusions
[Summarize Your Findings: Refer back to Step 1 and summarize your findings of the sample you selected.]
[Discuss: Discuss if you were surprised by the findings including why or why not.]
course_documents/MAT 240 House Listing Price by Region.xlsx
New England
House Listing Price Data by Region Source: https://www.realtor.com/research/data/
Regional sample (n = 1000)
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
NH merrimack New England $279,950 $142 2,016
MA hampden New England $239,950 $145 1,664
NH merrimack New England $283,525 $132 2,002
VT rutland New England $199,950 $111 1,857
ME kennebec New England $234,050 $128 1,768
VT chittenden New England $379,050 $181 2,050
ME androscoggin New England $217,443 $125 1,679
MA hampden New England $244,994 $148 1,726
NH rockingham New England $429,950 $198 2,066
CT litchfield New England $377,050 $166 2,185
MA hampshire New England $325,050 $179 1,907
NH grafton New England $229,050 $127 1,732
CT new london New England $290,000 $158 1,680
CT fairfield New England $746,550 $287 2,645
VT washington New England $297,050 $143 1,936
NH rockingham New England $461,950 $217 2,099
MA plymouth New England $509,550 $250 2,050
ME penobscot New England $158,864 $99 1,596
MA norfolk New England $597,500 $284 2,214
MA plymouth New England $469,050 $235 2,000
VT chittenden New England $397,086 $190 2,100
RI kent New England $274,950 $179 1,555
VT franklin New England $249,050 $131 1,799
MA worcester New England $319,950 $170 1,881
NH cheshire New England $226,550 $114 1,893
RI washington New England $544,950 $263 1,817
NH rockingham New England $434,950 $210 2,182
MA hampden New England $260,000 $153 1,749
CT windham New England $215,950 $129 1,632
CT middlesex New England $339,300 $169 1,832
VT franklin New England $209,050 $128 1,766
MA berkshire New England $389,050 $186 2,010
MA hampshire New England $369,500 $187 1,974
CT tolland New England $265,000 $143 1,830
NH merrimack New England $307,550 $140 2,195
ME penobscot New England $158,550 $100 1,583
NH grafton New England $279,050 $153 1,840
RI washington New England $549,950 $274 1,880
ME kennebec New England $210,000 $118 1,798
CT middlesex New England $329,050 $160 1,978
MA berkshire New England $387,050 $187 2,016
NH hillsborough New England $333,739 $158 2,061
NH merrimack New England $312,500 $148 2,214
MA berkshire New England $379,750 $184 2,031
VT washington New England $315,050 $151 1,900
MA middlesex New England $645,950 $287 2,237
MA franklin New England $247,550 $134 1,890
MA franklin New England $249,950 $148 1,792
VT rutland New England $209,550 $114 1,843
VT chittenden New England $366,550 $182 2,050
RI providence New England $252,500 $172 1,483
VT chittenden New England $377,950 $185 2,072
MA worcester New England $334,950 $179 1,938
ME androscoggin New England $192,450 $112 1,681
VT rutland New England $205,050 $106 1,839
MA hampden New England $238,007 $147 1,678
VT chittenden New England $384,950 $182 2,104
ME york New England $382,500 $230 1,742
ME kennebec New England $189,950 $118 1,700
MA franklin New England $248,500 $148 1,775
MA essex New England $577,050 $278 2,097
CT litchfield New England $332,500 $121 1,396
VT franklin New England $245,050 $131 1,800
NH grafton New England $236,550 $138 1,705
ME york New England $349,500 $211 1,762
CT new london New England $292,500 $157 1,800
MA suffolk New England $792,980 $750 1,263
CT fairfield New England $762,550 $292 2,653
MA barnstable New England $585,050 $306 1,898
CT fairfield New England $754,500 $291 2,774
RI newport New England $592,500 $323 1,982
MA franklin New England $249,950 $143 1,902
CT middlesex New England $329,050 $159 1,988
NH merrimack New England $330,050 $147 2,208
ME cumberland New England $389,950 $212 1,841
NH merrimack New England $320,050 $147 2,158
MA hampden New England $229,800 $143 1,635
MA berkshire New England $379,050 $186 2,016
ME york New England $349,950 $216 1,734
MA middlesex New England $627,450 $295 2,103
CT hartford New England $236,800 $141 1,682
ME penobscot New England $149,950 $96 1,550
MA barnstable New England $576,049 $299 1,904
CT middlesex New England $334,950 $163 1,722
VT washington New England $254,550 $139 1,820
ME penobscot New England $144,950 $92 1,574
MA worcester New England $305,000 $166 1,845
VT rutland New England $229,050 $117 2,000
NH grafton New England $209,050 $124 1,674
RI newport New England $580,050 $309 2,026
MA middlesex New England $619,500 $296 2,089
ME cumberland New England $369,407 $201 1,823
MA hampshire New England $345,050 $193 1,778
RI washington New England $499,050 $258 1,824
VT rutland New England $200,050 $116 1,882
VT windsor New England $349,050 $156 2,148
CT middlesex New England $330,050 $169 1,808
CT litchfield New England $338,300 $145 1,674
VT washington New England $249,950 $137 1,800
ME penobscot New England $149,550 $92 1,582
NH hillsborough New England $375,050 $174 2,157
MA bristol New England $419,950 $214 1,922
MA suffolk New England $799,050 $748 1,267
VT rutland New England $239,193 $121 1,996
MA hampshire New England $324,500 $179 1,958
MA suffolk New England $759,050 $666 1,351
NH grafton New England $227,050 $127 1,752
MA middlesex New England $699,050 $314 2,260
NH strafford New England $279,500 $148 1,872
NH cheshire New England $249,050 $129 1,854
ME kennebec New England $191,000 $107 1,700
ME cumberland New England $347,050 $192 1,800
MA bristol New England $350,000 $191 1,888
RI kent New England $277,500 $191 1,518
NH belknap New England $304,950 $166 1,842
VT franklin New England $242,500 $132 1,769
CT new london New England $317,050 $164 1,900
VT franklin New England $215,050 $128 1,728
ME york New England $379,564 $230 1,732
NH hillsborough New England $348,950 $167 2,058
MA berkshire New England $386,550 $185 2,044
ME cumberland New England $349,500 $189 1,871
MA essex New England $519,950 $264 2,000
ME york New England $360,050 $218 1,765
RI providence New England $259,950 $171 1,534
VT windsor New England $335,050 $153 2,158
VT windsor New England $299,050 $147 1,992
MA hampden New England $237,550
