MAT 240 Project Two Template 2

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Southern New Hampshire University *

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Apr 3, 2024

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Regional vs. National Housing Price Comparison Report 1 Report: Regional vs. National Housing Price Comparison Emily Lemieux Southern New Hampshire University

Regional vs. National Housing Price Comparison Report 2 Introduction Region : I have selected the East North Central region for this report Purpose : The overall purpose for this report would be able to determine if the East North Central regions housing prices on average are significantly less than the national housing markets average, and if the East North Central region average square footage that the national housing markets average price range. To start with this report, I created a random sample of 500 observations and with that I will also then move forward, with analyzing whether the average housing price in the EN central region are lower than the national market average. I will do this by using a 1-tail test and that will help me see if the average square footage in the east north central region is different from the overall national marketing average. I will do that by also using a 2-tail test. Sample: My chosen sample includes 5000 homes across the East north central region, as well as it also has the corresponding list prices and square footage for each house. Questions and type of test: With my sample, I will also be testing two hypothesis questions throughout my work. The population parameter for the first variable I will be moving forward to analyze is the average home listing price, and with that the hypothesis being tested is the average listing price for homes in the EN central region, with them being less than the national average. For me to be able to analyze this hypothesis I will be using the 1-tail test. The overall population parameter for the average square footage for homes in the EN central region is different, then the national average of the houses. To be able to do that, I will be moving forward with using a 2-tail test to help me analyze. The confidence level I wll be using for these hypothesis will be 0.95, and 0.05 significance level to help me calculate the confidence intervals where the true population men will truly lie within.

Regional vs. National Housing Price Comparison Report 3 1-Tail Test Hypothesis: he population parameter for the 1-tail test is average listing price Hypothesis:

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Regional vs. National Housing Price Comparison Report 4 Data analysis: The sample listing price data that I have above, seems to be skewed to the right due to some outliers that have listing prices that are above $335,050, and its skew is also very similar to the national market. However, the min, the max, the median, and the mean for the East North Central region seem to be lower than the national market data. For the test I’m using today all the assumptions and conditions have been met, even though the distribution appears to be

Regional vs. National Housing Price Comparison Report 5 more skewed to the right, the larger sample size of the 500 shows that the means are closer to a normal distribution that is being based on the Central Limit Theorem. Hypothesis Test Calculations: After I finished calculating everything, I was able to find out that the t-stat fir this 1-tail test is -23.87, and the p-value is6.191979E-82. Interpretation: Even with the p-value being significantly less than the significance level of 0.05, I will move forward to reject H0, because there is such strong and apparent evidence to be able to support the mean listing price being less the national average pricing. 2-Tail Test Hypotheses: The population parameter for the 1-tail test is average listing price Hypotheses:

Regional vs. National Housing Price Comparison Report 6 Data Analysis: Data Analysis: When they are compared to the national markets pricing per square footage, it is showing a more right-skewed due to having more outliers being above 2,2720 square feet. The national market is able to show that most homes have a square footage between 1,500- 1,875 and 1,875-2,250 (bimodal), while the East North Central region indicates most homes have a square footage between 1,530-1,700 (unimodal). When put into contrast the min, max, median, and mean for the EN central region are showed to be lower than the national market. For this test, all of the assumptions and conditions have been met. Even though the distribution is being distributed based on the Central limit Theorem.

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Regional vs. National Housing Price Comparison Report 7 Hypothesis Test Calculations: After I calculated everything, I was able to find that the t- statistic for this 2-tai; test is being shown to be -6.81, and the p value for the 2-tail test would come to be 2.86569E-11. Interpretation: With the p value being such less than the significance level of 0.05, I will move forward to reject H0, because I found there was not strong enough evidence that shows it is basically impossible for the mean square footage of the East North Central region to be the same to even equal to the national average which is 1,944 square foot. Comparison of the Test Results : For all my work today I used the CONFIDENCE.T formula in excel, for me to be able to calculate properly the margin of error. The margin of error total afterwards came to equal to 33.66 square footage. The confidence interval for the upper and lower bounds equal to 1793.71 sq. ft and also 1861.04 sq. ft. Final Conclusions Overall, I am at a 95% confident the average square footage for the East North Central region has come to land to be less than the national average pricing. Also, I am 95% confident that the average square footage for the East North Central region comes to equal out to be between 1793.71 and 1861.04 square feet. With that it is also falling in line with the confidence interval, I am though a little bit surprised by this outcome honestly. I’m surprised by this outcome because, my sample average, distribution and quartiles in previous report have come out to very closely resemble the population, where in this case this sample does not.

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