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Economics

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Feb 20, 2024

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Report: Regional vs. National Housing Price Comparison Kayla Zwart Southern New Hampshire University

Introduction I have been hired by the West North Central region real estate company to determine if my region’s housing prices and sq footage are significantly different from those in the national market. I will be analyzing the West North Central region mean in comparison to the national mean. By doing this analysis the real estate company will be informed of the best price point for

this specific region. Because house prices can significantly change based on the location of the house. For this analysis, I will compare mean house prices in my region to the mean house prices nationally. A random sample of n=500 will be chosen from the West North Central area. A hypothesis test will be conducted to determine whether the mean of the West North Central region is lower than the national market average. The first hypothesis will be evaluated to determine whether the regional house price is smaller than the national average. The second hypothesis will determine whether the average sq. Ft for my region is smaller than the national average. I will use a one-sample t-test, this being a one-tailed test, to determine whether the regional house price is larger than the national average. The 95% confidence interval for the mean sq. Ft. For homes in the North Central region will be constructed. 1-Tail Test The data being analyzed will include the house sizes for the West Central region. I will evaluate to see if the regional house price is smaller than the national average. The second hypothesis is that the regional sq. Ft. Is smaller than the national average. The sample consists of 500 randomly selected data points. My hypothesis will be evaluated at a 5% significance level.

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In this histogram of house sizes, it indicates the frequency of the house sizes in sq. Ft. Looking at the histogram the data is usually distributed and skewed towards the right significantly. Thus, m eaning the sample’s mean should be fairly like the mean of the national. This histogram is of the house price per sq. Ft. It shows a normal distribution. It is slightly skewed to the right as well. Meaning the regional sample is remarkably similar to the national mean.

The statistics presented in this table indicate various pieces of the data. The mean cost per sq. Ft. Is 126.4372. The standard deviation is 35.389. The variance is 125.37, the skewness is 0.69. Thus, indicating the values are significantly skewed to the left. The sq. Ft. For houses has a mean of 1919.37. The standard deviation is 371.44. The skewness is 0.038. Thus, indicating a left-hand skew as well. Interpretation: The p-value of cost per sq. Ft. And house size (sq. Ft. Per house) are 5.68163E- 57, 0.0523892. respectively. This means the cost per sq. Ft was high, Given the 5% level of significance. The null hypothesis can be rejected for cost per sq. Ft. However, the P-value for sq. Ft. Was a bit greater than 0.05. Meaning the null hypothesis cannot be rejected. This means there is a chance of the regional mean of house sizes could be higher than the national average. While the house price per sq. Ft. are likely to be less than the national average.

2-Tail Test The second test will determine if the national mean for the house size and listing price is smaller than the regional listing price and house size. I will be doing a two-tailed test to determine this hypothesis. The null hypothesis is the mean regional house size is smaller than the national mean house size. This histogram is of house sizes. It indicates the frequency of the house sizes in sq. Ft. Using the data from the histogram, the data is significantly skewed toward the right. This means the sample's mean should be extremely similar to the national mean.

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This histogram is of the prices per sq. Ft. It shows a normal distribution with a slight skew to the right. This also means that the sample is similar to the national mean.

The graph above includes various data points. Including the mean cost per sq. Ft. Being, 126.4372. The standard deviation is 35.389. While the variance is 1252.37. The skewness is 0.69. Meaning there is a significant left-hand skew. The house sq. Ft. Had a mean of 1919.37. The standard deviation is 371.44. The skewness is 0.038. This indicates a left-hand skew as well Looking at the graph above the p-values obtained, the cost per sq. Ft. Had much lower p-values. Lower than the 0.05 level of significance. This means that we will reject the hypothesis. When looking at the sq, ft. Or house, the p-value is much higher than 0.05. This means we cannot reject the hypothesis. The mean of the West North Central region can be considered equal to the national listing price. I say this with a 95% level of accuracy. On the other hand, mean house sizes in my region were not equal to the national mean house size. The method I used to calculate the graph above was the internal Excel confidence function: =CONFIDENCE.NORM(Alpha, Standard Deviation, Sample Size)

From what I found above we can see that the mean house cost per sq. Ft. Is 126.4372615 ± 2.831641898. Along with the mean sq. Dt. For the region is 1919.364643 ± 29.72119052. Final Conclusions My region's house prices were remarkably similar to national prices. When it comes to the house sizes, they were found not to be smaller or similar, meaning they were most likely larger than the national average. My analysis results did not surprise me. Seeing as this region is mainly populated by people of the middle class. They prefer average prices for larger houses.

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