7-3 Project Two Regional vs. National Housing Price Comparison Report

7-3 Project Two Regional vs. National Housing Price Comparison Report

Shanon Beck

MAT-240 Applied Statistics

October 15th, 2023

Report: Regional vs. National Housing Price Comparison

Shanon Beck

Southern New Hampshire University

Introduction

The purpose of this report is to determine whether or not the average housing prices and housing square footage in the Mid-Atlantic region are lower than the national market. In order to do this, we took a sample of 500 houses from the Mid-Atlantic region and will use that sample to compare the housing prices of the Mid-Atlantic region to the national market, as well as the square footage of the given housing sample. In order to get the housing sample, we took all of the houses from the Mid-Atlantic region and assigned them a random value between 0 and 1 using the RAND() function; we then sorted the random values from lowest to highest and took the first 500 from that list, excluding duplicate numbers. For our report, we have two distinct hypotheses we would like to confirm or deny. The first is our t-test on the Mid-Atlantic Sample Housing Prices. Given the variable, our Null hypothesis is HO: μ = 288407, while our alternative hypothesis is H1: μ < 288407, which is a 1-tailed test. Our second t-test is the Mid-Atlantic sample square footage, with our null hypothesis being HO: μ = 1944 and our alternative hypothesis being H1: μ ≠ 1944, which uses a 2-tailed t-test. In order to solve our t-test hypothesis, we will determine the confidence level and take note of the probabilities of those hypotheses being true.

For our first variable (housing price), we have our 1-Tail Test, with our Null hypothesis being HO: μ = 288407 and our alternative hypothesis being H1: μ < 288407. Our significance level is 95%.

Data Anylsis

Compared to our national market, our sample data is skewed heavily to the right, while the national data is only moderately skewed to the right. Our average mean is lower than the national mean of 288,407 (-45,034). Our test is a 1-tailed test, with a t-statistic of 5.43, and a p-value of 0. 00000004326036. Given this, our confidence value is 95% that our median listing price falls between $227,090 and $259,657. We reject the null hypothesis of HO: μ = 288407 based on the strong evidence that the alternative hypothesis is correct.

2-Tailed Test

Four our 2-Tailed Test, we tested whether or not the average square footage of our region is lower than the national market. Our null hypothesis is HO: μ = 1944, while our alternative hypothesis is H1: μ ≠ 1944.

Compared to our national market, our average mean is lower (1,944), with similar histograms, our t-statistic if -16.83, while our p-value is 0. Given this information, we have a confidence level of 95% that the average square footage falls between 1,664 and 1,722; therefore we reject or null hypothesis on the basis that it is basically impossible that the square footage equals 1944.

Final Conclusion

Our final conclusion is that both the average listing price and average square footage in the Mid-Atlantic region is smaller than that of the national market. I am not surprised by this given that the Mid-Atlantic region (where I live) has a long history, hundreds of years back when houses were on-average smaller, while rest of the country is relatively new compared to the Mid-Atlantic States.