Competency In This Project, You Will Demonstrate Your Master ✓ Solved
Competency In this project, you will demonstrate your mastery of
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.
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?
Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director.
The final report should include definitions of the sample, hypotheses, data analysis, interpretation of results, and final conclusions.
Paper For Above Instructions
Introduction
The purpose of this analysis is to evaluate the housing market in a specified region of the United States and compare it with national averages concerning housing prices and square footage. Through this project, I will apply statistical techniques to test two primary hypotheses regarding the housing market.
A random sample of 100 observations will be taken from the housing sales data specific to the defined region. The sample will represent various states within the region and include data collected over the past 12 months. This sampling will provide a comprehensive overview of the current market conditions.
Hypothesis Overview
For the first hypothesis, the question is: "Are housing prices in your regional market higher than the national market average?" This will involve a one-tailed test. The null hypothesis (H0) posits that the mean housing price in the region is less than or equal to the national average. The alternative hypothesis (Ha) states that the mean housing price in the region is greater than the national average.
The population parameter in this situation is the average housing price in the region. The inference test used will be a one-sample t-test for means. The appropriate test statistic measured will be the t-value, which will be calculated based on the difference between the sample mean and the national average, divided by the standard error of the sample mean.
Level of Confidence
To address this question in a statistically significant manner, a significance level of α = 0.05 will be set. This level indicates that we will accept a 5% chance of rejecting the null hypothesis when it is true.
Data Analysis
The data analysis process starts with confirming assumptions are not violated for our hypothesis tests. Graphical displays will include histograms that demonstrate the distribution of housing prices within our sampled region. Summary statistics will be compiled to include sample size (n = 100), mean, median, and standard deviation.
After summarizing the sample data and comparing the center, spread, and shape of the distributions with national information, we will check the normality condition and other conditions relevant to the data analysis.
Hypothesis Test Calculations
We will calculate the hypothesis test statistics including the t statistic. These calculations will utilize the equation for the t statistic based on our sample mean, national average, and standard deviation. The p-value will then be determined to evaluate statistical significance for this hypothesis test.
Interpretation
Using the results obtained, we will interpret the hypothesis test results based on the calculated p-value. If the p-value is less than 0.05, we will reject the null hypothesis, indicating that housing prices in our region are statistically significantly higher than the national average. In the conclusion section, we will discuss these findings in the context of our hypothesis.
Two-Tailed Test Hypotheses
The second hypothesis question is: "Is the square footage for homes in your region different than the average square footage for homes in the national market?" This involves a two-tailed test, with the null hypothesis (H0) asserting that the mean square footage in the region is equal to the national average. The alternative hypothesis (Ha) claims that the mean square footage in the region is different from the national average.
We will follow similar steps for data analysis and hypothesis test calculations as stated in the first hypothesis. I will ensure the data displayed represents a robust summary through graphical includes and summary tables.
Comparison of Test Results
Finally, this section will interpret the 95% confidence interval and relate its significance to our overall analysis.
Final Conclusions
In summarizing the findings, I will revisit the analysis' introduction and highlight key insights derived from the sample data. I will also discuss whether any results were surprising, providing reasoning based on the national averages encountered during the project.
References
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- Keller, G. (2018). Statistics for Management and Economics. Cengage Learning.
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- Rosner, B. (2011). Fundamentals of Biostatistics. Cengage Learning.
- Siegel, A. F. (2017). Practical Business Statistics. Elsevier.
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- Wackerly, D., Mendenhall, W., & Beaver, R. (2008). Mathematical Statistics with Applications. Thomson Brooks/Cole.