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:

1. Are housing prices in your regional market lower than the national market average?
2. Is the square footage for homes in your region different than the average square footage for homes in the national market?
3. 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

1. Region: Start by picking one region from the following list of regions: Is below West South Central
2. Purpose: What is the purpose of your analysis?
3. Sample: Define your sample. Take a random sample of 500 house sales for your region.
   1. Describe what is included in your sample (i.e., states, region, years or months).
4. 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:
   1. Describe the population parameter for the variable you are analyzing.
   2. Describe your hypothesis in your own words.
   3. Identify the hypothesis test you will use (1-Tail or 2-Tail).
5. Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem.

1-Tail Test

1. Hypothesis: Define your hypothesis.
   1. Define the population parameter.
   2. Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.
   3. Specify your significance level.
2. 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.
   1. Provide at least one histogram of your sample data.
   2. 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])
   3. 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.
   4. Check the conditions.
      1. Determine if the normal condition has been met.
      2. 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.
3. Hypothesis test calculations: Complete hypothesis test calculations.
   1. Calculate the hypothesis statistics.
      1. 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.
      2. Calculate the probability (p value). Note: This calculation is done with the T.DIST function in Excel: =T.DIST([test statistic], [degree of freedom], True) The degree of freedom is calculated by subtracting 1 from your sample size.
4. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
   1. Relate the p value and significance level.
   2. Make the correct decision (reject or fail to reject).
   3. Provide a conclusion in the context of your hypothesis.

2-Tail Test

1. Hypotheses: Define your hypothesis.
   1. Define the population parameter.
   2. Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.
   3. State your significance level.
2. 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.
   1. Provide at least one histogram of your sample data.
   2. 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])
   3. 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.
   4. Check the assumptions.
      1. Determine if the normal condition has been met.
      2. 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.
3. Hypothesis test calculations: Complete hypothesis test calculations.
   1. Calculate the hypothesis statistics.
      1. 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.]
      2. Determine the probability (p value). Note: This calculation is done with the TDIST.2T function in Excel: =T.DIST.2T([test statistic], [degree of freedom]) The degree of freedom is calculated by subtracting 1 from your sample size.
4. Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
   1. Compare the p value and significance level.
   2. Make the correct decision (reject or fail to reject).
   3. Provide a conclusion in the context of your hypothesis.
5. 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?
   1. Calculate and report the 95% confidence interval. Show or describe your method of calculation.

Final Conclusions

1. Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language.
2. Discuss: Discuss whether you were surprised by the findings. Why or why not?

Region: [Clearly specify the region you picked from the list of regions mentioned in the Directions (West South Central, West North Central, East South Central, East North Central, Mid Atlantic).]

Purpose: [Define the purpose of the report.]

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 in the learning management system) and the appropriate type of test hypothesis for each.]

[First hypothesis:Describe the population parameter for the variable you are analyzing.]

[First hypothesis:Describe your hypothesis in your own words.]

[First hypothesis: Identify the hypothesis test you will use (1-Tail or 2-Tail).]

[Second hypothesis:Describe the population parameter for the variable you are analyzing.]

[Second hypothesis:Describe your hypothesis in your own words.]

[Second hypothesis: 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 the population parameter.]

Hypothesis: [Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.]

Hypothesis: [Specify your significance level.]

Data analysis:[Provide at least one histogram of your sample data.]

Data analysis:[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])

Data analysis:[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 in the learning management system). Note: For shape, think about the distribution: skewed or symmetric.]

Data analysis:[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.]

Hypothesis Test Calculations: [Calculate the probability (pvalue). Note: This calculation is done with the T.DIST function in Excel:

=T.DIST([test statistic], [degree of freedom], True).

The degree of freedom is calculated by subtracting 1 from your sample size.]

Interpretation:[Compare the pvalue and significance level.]

Interpretation:[Make the correct decision (reject or fail to reject).]

Interpretation:[Provide a conclusion in the context of your hypothesis.]

2-Tail Test

Hypotheses: [Define the population parameter.]

Hypotheses: [Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.]

Hypotheses: [State your significance level.]

Data Analysis: [Provide at least one histogram of your sample data.]

Data Analysis: [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]) ]

Data Analysis: [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.]

Data Analysis: [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.]

Hypothesis Test Calculations: [Calculate the probability (pvalue). Note: This calculation is done with the TDIST.2T function in Excel: =T.DIST.2T([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.]

Interpretation:[Relate the pvalue and significance level.]

Interpretation:[Make the correct decision (reject or fail to reject).]

Interpretation:[Provide a conclusion in context to your hypothesis.]

Comparison of the Test Results:[Calculate and report the 95% confidence interval. Show or describe the method of calculation.]

Final Conclusions

Summarize Your Findings:[In one paragraph, summarize your findings in clear and concise plain language.]

Discuss: [Discuss if you were surprised by the findings including why or why not.]

Region State County listing $'s per listing

Price Square foot Price

West North Central MN Anoka 292,300 $201 1,455

West north central MO St.charles 430,000 $187 2,302

West North central MO platte 269,200 $184 1,467

West north central ia Johnson 643,300 $160 1,467

west north central ia scott 286,600 $191 1,501

west north central Mn clay 350,900 $163 2,158

west north central ks saline 245,200 $142 1,721

west north central ks riley 356,900 $158 2,261

west north central nd grand forks 390,700 $173. 2,258

West North Central	KS	Wyandotte	259,500	$159	1,631
West North Central	ia	Pottawattamie	297,400	$186	1,603
West North Central	nd	Cass	259,700	$179	1,454
West North Central	Mo	St. Charles	309,400	$143	2,158
West North Central	nd	Ward	402,800	$252	1,599
West North Central	mn	Sherburne	361,600	$177	2,041
West North Central	nd	Burleigh	345,300	$162	2,132
West North Central	mo	Clay	294,000	$177	1,659
West North Central	mo	Newton	322,600	$146	2,205
West North Central	ne	Buffalo	360,800	$152	2,375
West North Central	mn	Winona	270,600	$149	1,816
West North Central	sd	Minnehaha	623,500	$162	3,854
West North Central	mo	Johnson	371,300	$155	2,388
West North Central	ia	cerro gordo	361,000	$193	1,869
West North Central	mn	Dakota	262,800	$144	1,824
West North Central	mo	Platte	289,100	$189	1,530
West North Central	ks	Johnson	369,000	$155	2,387
West North Central	ia	Warren	402,400	$199	2,022
West North Central	ia	Linn	745,500	$165	4,531
West North Central	mn	Hennepin	353,300	$158	2,236
West North Central	nd	grand forks	394,400	$169	2,338
West North Central	mo	saint louis city	253,900	$156	1,623
West North Central	sd	Lincoln	543,800	$158	3,431
West North Central	mn	Carver	290,500	$156	1,868
West North Central	ks	Shawnee	247,100	$164	1,511
West North Central	ks	Butler	268,300	$160	1,677
West North Central	mn	crow wing	263,200	$164	1,602
West North Central	sd	Pennington	233,600	$146	1,600
West North Central	mo	cape girardeau	292,100	$162	1,798
West North Central	mo	Franklin	310,900	$143	2,173
West North Central	ne	Douglas	278,700	$191	1,458
West North Central	mo	Boone	418,900	$179	2,341
West North Central	ia	Polk	720,300	$16 2	4,459
West North Central	ia	Clinton	301,200	$214	1,405
West North Central	mn	Scott	426,800	$181	2,361
West North Central	mo	saint louis city	273,200	$172	1,592
West North Central	ks	Sedgwick	303,400	$194	1,563
West North Central	mn	otter tail	315,400	$173	1,828
West North Central	ia	Woodbury	245,500	$139	1,761
West North Central	mn	Washington	282,100	$172	1,642
West North Central	ia	pottawattamie	815,200	$157	5,182
West North Central	ia	Linn	425,300	$188	2,265
West North Central	ia	Polk	393,600	$192	2,048
West North Central	ne	Lancaster	354,400	$149	2,379
West North Central	ne	Sarpy	273,200	$164	1,665
West North Central	mo	Greene	388,900	$166	2,341
West North Central	ne	Lancaster	300,700	$191	1,574
West North Central	mo	Jasper	319,600	$176	1,813
West North Central	ks	Leavenworth	321,700	$188	1,712
West North Central	mo	Cass	291,200	$180	1,620
West North Central	mo	st. francois	325,500	$167	1,951
West North Central	mn	Olmsted	211,000	$148	1,427
West North Central	mo	Cole	408,200	$187	2,183
West North Central	ne	Douglas	324,500	$162	2,006
West North Central	mn	Wright	420,500	$179	2,351
West North Central	ia	Dubuque	331,100	$180	1,839
West North Central	mn	Goodhue	340,200	$148	2,296
West North Central	mo	st. louis	387,900	$195	1,994
West North Central	mn	Stearns	362,000	$163	2,223
West North Central	ne	Hall	276,900	$154	1,794
West North Central	mn	Ramsey	344,400	$166	2,073
West North Central	sd	Lincoln	461,000	$195	2,359
West North Central	ia	Story	930,400	$178	5,223
West North Central	mo	Lincoln	260,100	$144	1,804
West North Central	mo	st. francois	355,600	$200	1,774
West North Central	mo	Taney	264,200	$187	1,410
West North Central	ne	Hall	324,900	$185	1,756
West North Central	mn	st. louis	337,200	$163	2,066
West North Central	ia	Dallas	401,900	$184	2,183
West North Central	ks	Reno	402,000	$196	2,052
West North Central	mn	Chisago	309,900	$196	1,583
West North Central	ia	Story	395,000	$170	2,325
West North Central	ia	black hawk	286,700	$204	1,404
West North Central	mn	Rice	263,800	$187	1,412
West North Central	ia	Johnson	421,400	$195	2,165
West North Central	ks	Douglas	267,600	$179	1,498
West North Central	mo	Buchanan	266,200	$168	1,589
West North Central	nd	Cass	389,000	$183	2,120
West North Central	nd	Burleigh	428,200	$178	2,400
West North Central	ne	Sarpy	510,600	$149	3,431
West North Central	mo	st. louis	440,100	$197	2,229
West North Central	mo	Jackson	409,400	$181	2,262
West North Central	mo	Christian	351,600	$197	1,786
West North Central	sd	Minnehaha	414,900	$217	1,908
West North Central	nd	ward	370,900	$175	2,125
West North Central	mn	blue earth	315,900	$208	1,518
West North Central	mo	jefferson	324,000	$183	1,766
West North Central	ia	scott	869,200	$151	5,774
West North Central	mo	taney	351,700	$194	1,816
West North Central	ne	buffalo	471,600	$197	2,393
West North Central	ia	warren	745,100	$140	5,315