Category: Mathematics and Statistics : Statistics

Scenario
You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople just returned to the office with a newly designed advertisement. The average cost per square foot of home sales based on this advertisement is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280. In other words, he claims that the newly designed advertisement would result in higher average cost per square foot in the Pacific Region. He wants you to make sure he can make that statement before approving the use of the advertisement. In order to test his claim, you will generate a random sample of size 750 houses using data for the Pacific region and use this data to perform a hypothesis test.
Prompt
Generate a sample of size 750 houses using data for the Pacific region. Then, design a hypothesis test and interpret the results using significance level α = .05. You will work with this sample in this assignment. Briefly describe how you generated your random sample.
Use the House Listing Price by Region document to help support your work on this assignment. You may also use the Descriptive Statistics in Excel PDF and Creating Histograms in Excel PDF tutorials for support.
Specifically, you must address the following rubric criteria, using the Module Five Assignment Template Word Document
Introduction: Describe the purpose of this analysis and how you generated your random sample size of 750 houses.
Hypothesis Test Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test.
Define your population parameter.
Write the null and alternative hypotheses.
Specify the name of the test you will use.
Identify whether it is a left-tailed, right-tailed, or two-tailed test.
Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and identify the test significance level.
Provide the descriptive statistics (sample size, mean, median, and standard deviation).
Provide a histogram of your sample.
Summarize your sample by writing a sentence describing the shape, center, and spread of your sample.
Check whether the assumptions to perform your identified test have been met.
Identify the test significance level. For example, α = .05.
Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis.
Calculate the sample mean and standard error.
Determine the appropriate test statistic, then calculate the test statistic.
Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean (Pacific), and the target is 280.
Calculate the p value using one of the following tests.
Choose your test from the following:
=T.DIST.RT([test statistic], [degree of freedom]): right-tailed test
=T.DIST([test statistic], [degree of freedom], 1): left-tailed test
=T.DIST.2T([test statistic], [degree of freedom]): two-tailed test
Note: The degree of freedom is calculated by subtracting 1 from your sample size.
Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.
Test Decision: Compare the relationship between the p value and the significance level, and decide to reject or fail to reject the null hypothesis.
Compare the relationship between the p value and significance level.
Decide to reject or fail to reject the null hypothesis.
Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance.
Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.
You can use the following tutorial that is specifically about this assignment:

I have already done the required excel sheet, I just need the report done with the template provided.
MAT 240 Project One Guidelines and Rubric
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techniques to address research problems
Perform regression analysis to address an authentic problem
Overview
The purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.
Scenario
You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.
Directions
Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate Data Spreadsheet spreadsheet (both found in the Supporting Materials section) for your statistical analysis.
Note: Present your data in a clearly labeled table and using clearly labeled graphs.
Specifically, include the following in your report:
Introduction
Describe the report: Give a brief description of the purpose of your report.
Define the question your report is trying to answer.
Explain when using linear regression is most appropriate.
When using linear regression, what would you expect the scatterplot to look like?
Explain the difference between predictor (x) and response (y) variables in a linear regression to justify the selection of variables.
Data Collection
Sampling the data: Select a random sample of 50 houses. Describe how you obtained your sample data (provide Excel formulas as appropriate).
Identify your predictor and response variables.
Scatterplot: Create a scatterplot of your predictor and response variables to ensure they are appropriate for developing a linear model.
Data Analysis
Histogram: Create a histogram for each of the two variables.
Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
Interpret the graphs and statistics:
Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for house sales and square footage.
Compare and contrast the center, shape, spread, and any unusual characteristic for your sample of house sales with the national population (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Determine whether your sample is representative of national housing market sales.
Develop Your Regression Model
Scatterplot: Provide a scatterplot of the variables with a line of best fit and regression equation.
Based on your scatterplot, explain if a regression model is appropriate.
Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
Identify any possible outliers or influential points and discuss their effect on the correlation.
Discuss keeping or removing outlier data points and what impact your decision would have on your model.
Calculate r: Calculate the correlation coefficient (r).
Explain how the r value you calculated supports what you noticed in your scatterplot.
Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.
Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
Interpret regression equation: Interpret the slope and intercept in context. For example, answer the questions: what does the slope represent in this situation? What does the intercept represent? Revisit the Scenario above.
Strength of the equation: Provide and interpret R-squared.
Determine the strength of the linear regression equation you developed.
Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the assumed square footage of your home at 1500 square feet.
Conclusions
Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
Did you see the results you expected, or was anything different from your expectations or experiences?
What changes could support different results, or help to solve a different problem?
Provide at least one question that would be interesting for follow-up research.
You can use the following tutorial that is specifically about this assignment. Make sure to check the assignment prompt for specific numbers used for national statistics. The videos may use different national statistics. You should use the national statistics posted with this assignment.

You will now add information from this week’s materials to the attached  Research Chart.
In the corresponding section, provide the name(s) of the method you reviewed, its primary use and when it should be used, strengths and limitations of the method, ethical considerations, and one example of when the method could be used (include your interests or something more general).
Length: Updated research chart, not including title and reference pages. Be sure to cite this week’s resources used in your assignment.