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 regions 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?
Analyzing Housing Market Data for a Region in the United States
Introduction
In this analysis, we will investigate whether housing prices and square footage in a specific region of the United States differ significantly from the national market averages. We will use appropriate sampling and statistical methods to address the questions posed by the regional sales director.
Hypotheses
1. Housing Prices:
- Null Hypothesis ($H_0$): The average housing prices in the regional market are not significantly lower than the national market average.
- Alternative Hypothesis ($H_1$): The average housing prices in the regional market are significantly lower than the national market average.
2. Square Footage:
- Null Hypothesis ($H_0$): The average square footage for homes in the region is not significantly different from the national market average.
- Alternative Hypothesis ($H_1$): The average square footage for homes in the region is significantly different from the national market average.
Sampling and Statistical Methods
1. Housing Prices Analysis:
- We will collect a random sample of housing prices from both the regional market and the national market.
- Conduct a two-sample t-test to compare the mean housing prices between the regional and national markets.
- Calculate the p-value to determine the significance of the price difference.
2. Square Footage Analysis:
- Obtain a random sample of square footage data for homes in the region and the national market.
- Perform a two-sample t-test to assess whether the mean square footage in the region differs significantly from the national average.
- Calculate the 95% confidence interval for the square footage values in the regional market.
Results and Interpretation
1. Housing Prices Comparison:
- After conducting the t-test, if the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis and conclude that housing prices in the regional market are significantly lower than the national market average.
2. Square Footage Analysis:
- If the t-test results indicate a significant difference in square footage between the region and the national market, we reject the null hypothesis in favor of the alternative hypothesis.
- The 95% confidence interval for square footage in the regional market will provide a range of values within which we can be 95% confident that the true mean square footage lies.
Conclusion
By employing appropriate sampling techniques and statistical methods, we can provide valuable insights into whether housing prices and square footage in a specific region of the United States differ significantly from national market averages. This analysis will help inform decision-making processes for real estate professionals and contribute to a better understanding of regional housing market dynamics.