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([data range], [quartile number])
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([test statistic], [degree of freedom], 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([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.
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([test statistic], [degree of freedom]) 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?
Category: Mathematics and statistics
The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.
B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.
Bronze Package – Sample size of 100 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500
Cost for service to B&K: $2,000
Silver Package – Sample size of 1,000 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750
Cost for service to B&K: $10,000
Gold Package – Sample size of 4,000 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900
Cost for service to B&K: $25,000
The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.
In other words, which option is preferable?
Spending more on data collection and having a smaller margin of error
Spending less on data collection and having a larger margin of error
Choosing an option somewhere in the middle
For your initial post:
Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for all packages. “I am [#] % confident the true mean . . . [in context].”
Explain the factors that went into your recommendation, including a discussion of the margin of error
Instructions
Link to article:
https://cdn.inst-fs-iad-prod.inscloudgate.net/970a3430-17e1-4a16-9492-6a3508e19b32/May%202024_Trends%20of%20Health%20Funding.pdf?token=eyJhbGciOiJIUzUxMiIsInR5cCI6IkpXVCIsImtpZCI6ImNkbiJ9.eyJyZXNvdXJjZSI6Ii85NzBhMzQzMC0xN2UxLTRhMTYtOTQ5Mi02YTM1MDhlMTliMzIvTWF5JTIwMjAyNF9UcmVuZHMlMjBvZiUyMEhlYWx0aCUyMEZ1bmRpbmcucGRmIiwidGVuYW50IjoiY2FudmFzIiwidXNlcl9pZCI6Ijk4NDQwMDAwMDAwMTg4NjA0IiwiaWF0IjoxNzE2NDcyMTk1LCJleHAiOjE3MTY1NTg1OTV9.frOdep-7lOjhIkDeYgzWGKZhRZY3uOcOhit_lb2T5D8qCZYY-Z8yNezjQUJV89j_iAkhJEwcw5vCbEmWu2auoA&download=1&content_type=application%2Fpdf
Link to textbook:
https://openstax.org/details/books/introductory-business-statistics
Part 1:
Your instructor will provide you with a scholarly article. The article will contain at least one graph and/or table. Please reach out to your instructor if you do not receive the article by Monday of Week 3.
Part 2:
Title your paper: “Review of [Name of Article]”
State the Author:
Summarize the article in one paragraph:
Post a screenshot of the article’s frequency table and/or graph.
Example:
Frequency Distribution -OR- Graph
Answer the following questions about your table or graph.
What type of data does the graph, chart, or table from your screenshot above display (Quantitative or Qualitative data)?
Explain how you came to that conclusion.
What type of graph, table, or chart did you choose from your screenshot above display (bar graph, histogram, stem & leaf plot, etc.)?
What characteristics make it this type (you should bring in material that you learned in the course)?
Describe the data displayed in your graph, table, or chart from your screenshot above. What is the graph displaying in the context of the article?
Draw a conclusion about the data from the graph, table, or chart from your screenshot above in the context of the article. Make an inference based on the data displayed.
How else might this data have been displayed?
Pick two alternate graphs/charts/tablesthat could be used to display the same data as your selected chart/graph/table from your screenshot above. List the pros and cons of these alternative graphs.
Explain how the graphs/charts/tables that you selected above (Part E) would be structured to display the data in the article.
Give the full APA reference of the article you are using for this lab.
Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 3: Lab”.
Scenario
Smart businesses in all industries use data to provide an intuitive analysis of how they can get a competitive advantage. The real estate industry heavily uses linear regression to estimate home prices, as cost of housing is currently the largest expense for most families. Additionally, in order to help new homeowners and home sellers with important decisions, real estate professionals need to go beyond showing property inventory. They need to be well versed in the relationship between price, square footage, build year, location, and so many other factors that can help predict the business environment and provide the best advice to their clients.
Prompt
You have been recently hired as a junior analyst by D.M. Pan Real Estate Company. The sales team has tasked you with preparing a report that examines the relationship between the selling price of properties and their size in square feet. You have been provided with a Real Estate Data Spreadsheet spreadsheet that includes properties sold nationwide in recent years. The team has asked you to select a region, complete an initial analysis, and provide the report to the team.
Note: In the report you prepare for the sales team, the response variable (y) should be the listing price and the predictor variable (x) should be the square feet.
Specifically you must address the following rubric criteria, using the Module Two Assignment Template:
Generate a Representative Sample of the Data
Select a region and generate a simple random sample of 30 from the data.
Report the mean, median, and standard deviation of the listing price and the square foot variables.
Analyze Your Sample
Discuss how the regional sample created is or is not reflective of the national market.
Compare and contrast your sample with the population using the National Summary Statistics and Graphs Real Estate Data PDF document.
Explain how you have made sure that the sample is random.
Explain your methods to get a truly random sample.
Generate Scatterplot
Create a scatterplot of the x and y variables noted above. Include a trend line and the regression equation. Label the axes.
Observe patterns
Answer the following questions based on the scatterplot:
Define x and y. Which variable is useful for making predictions?
Is there an association between x and y? Describe the association you see in the scatter plot.
What do you see as the shape (linear or nonlinear)?
If you had a 1,800 square foot house, based on the regression equation in the graph, what price would you choose to list at?
Do you see any potential outliers in the scatterplot?
Why do you think the outliers appeared in the scatterplot you generated?
What do they represent?