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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

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