MAT 240 Project Two2

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Economics

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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 Tiarre Crawford Southern New Hampshire University

Regional vs. National Housing Price Comparison Report 2 Introduction Region : I have been selected to represent the Mid-Atlantic real estate company. Purpose : I have been hired to determine if the housing prices in the Mid- Atlantic are lower than the national market average. So, the purpose of my report would be to determine the relationship between housing prices and housing square footage in my region by using a sample size of 500 randomly selected home listings to then compare it with the national markets’ housing prices and housing square footage. I will use the data I collect to determine if my hypothesis is indeed true or indeed not true. Also, to decide the range of values of square footage for homes in my regional market.

Regional vs. National Housing Price Comparison Report 3 State County Region House listing price Cost per square foot Square footage PA delaware Mid Atlantic $205,050 $121 1,600 NJ hunterdon Mid Atlantic $499,950 $50 725 PA york Mid Atlantic $237,500 $111 1,995 NY ulster Mid Atlantic $319,050 $157 2,088 NY ulster Mid Atlantic $300,050 $154 2,093 PA philadelphiaMid Atlantic $259,950 $192 1,243 NJ atlantic Mid Atlantic $249,050 $79 1,072 NY orange Mid Atlantic $275,182 $145 1,962 NY herkimer Mid Atlantic $174,500 $99 1,654 NY putnam Mid Atlantic $417,850 $201 2,059 PA pike Mid Atlantic $187,293 $89 2,104 NJ cape may Mid Atlantic $425,050 $150 880 NJ atlantic Mid Atlantic $239,500 $84 1,112 NJ salem Mid Atlantic $121,336 $82 1,440 PA philadelphiaMid Atlantic $255,000 $186 1,228 NY oswego Mid Atlantic $120,050 $79 1,573 PA crawford Mid Atlantic $125,000 $74 1,612 NY montgomeryMid Atlantic $149,950 $88 1,756 PA chester Mid Atlantic $435,500 $160 2,575 NY livingston Mid Atlantic $129,500 $72 1,717 PA lebanon Mid Atlantic $216,500 $116 1,755 PA montgomeryMid Atlantic $355,000 $157 2,035 PA philadelphiaMid Atlantic $259,050 $190 1,244 PA bucks Mid Atlantic $400,047 $177 2,251 NY onondaga Mid Atlantic $199,050 $104 1,793 PA schuylkill Mid Atlantic $83,750 $40 1,496 NY wayne Mid Atlantic $169,250 $99 1,690 NY niagara Mid Atlantic $134,279 $93 1,533 NY niagara Mid Atlantic $149,050 $97 1,506 NY clinton Mid Atlantic $159,950 $91 1,742 NY ulster Mid Atlantic $285,050 $147 1,992

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Regional vs. National Housing Price Comparison Report 4 National Avg Lisisting Price $288,407 Sample Mean $258,047 sample Std Dev 222,677.7 $ standard Error 9,958.45 $ National Square Footage 1,944 Sample Mean 1,700.57 Sample Std. Dev -352.42 Standard erro -15.76089599 Sample: The above chart is a depiction of my 500 randomly sampled home listings from my Mid – Atlantic region. In this chart, you can see the states and counties from which the data are taken from. There is also a representation of average housing listing prices as well as average square footage and cost per square footage. Showing the mean, median, standard deviation, and standard error for both Mid-Atlantic and National markets expressing the differences between the two. Questions and type of test: The first question I need to address would be rather the average housing prices in the Mid- Atlantic Market are lower than those of the National Market. To find a conclusion for this hypothesis I will conduct a 1-Tailed Test. The next question I tend to find a solution to is whether the square footage for homes in the Mid-Atlantic displays any differences from the average square footage for homes in the National market in which I will conduct a 2-Tailed Test. I will use confidence intervals and estimation from findings to compare and determine if my initial hypothesis stands correct or if the alternative hypothesis determines a different outcome. For these two tests I will use a significance level of a=.05

Regional vs. National Housing Price Comparison Report 5 1-Tail Test Hypothesis: My null hypothesis (H0) will represent that the U=Mid- Atlantic mean listing price, is equal to the $288,407 mean listing price of the National region. The alternative hypothesis (H1) will determine whether the Mid- Atlantic mean listing price is less than the $288,407 mean listing price in the National region. I will be using a significance level of a=.05 Quartile 1 142,913 $ Quartile 3 281,263 $ Data Analysis: When looking at the data table you can see that the national average($288,407) listing price is significantly higher than the Mid-Atlantic average ($258,047) listing price. When u look at the histogram it shows a representation of a left-skewed distribution with a center around the population median of approximately $196,823, there are a few gaps in areas in which no data is present. Quartile three shows that 75% of the data in the Mid- Atlantic falls below the average national listing price. The national region histogram is also left skewed, yet it has fewer

Regional vs. National Housing Price Comparison Report 6 gaps and a center of around $ 249,940. It seems that the normal conditions have been met. Yet to determine if it stands correct, I will have to produce some calculations to test my hypothesis. Hypothesis Test Calculations: Interpretation: Since the P-value is less than the level of significance(0.05) I will reject the null hypothesis(H0) which states that the average listing price for the Mid-Atlantic region is equal to the average listing price of the national region and accept the alternative(H1). There is evidence t hat my alternative hypothesis (H1) proves that the average listing price in the Mid-Atlantic region is lower than in the National region. 2-Tail Test Hypotheses : My null hypothesis (H0) will represent that the U=Mid- Atlantic average square footage is equal to the 1,944 average square footage of the National region. The alternative hypothesis (H1) will determine if the Mid- Atlantic average square footage is not equal to the average 1,944 square footage in the National region. I will be using a significance level of a=.05 Data Analysis:

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Regional vs. National Housing Price Comparison Report 7 National Square Footage 1,944 Sample Mean 1,700.57 Sample Std. Dev -352.42 Standard erro -15.76089599 Q1 1550 Q3 1902.25 My sample data on the histogram above show a normal distribution that gives a bell-shaped appearance. Its center is around the median square footage of 1,733. From looking at the table we can see that the national region square footage average is slightly higher than the standard square footage in the Mid-Atlantic region. Compared to the national region histogram the two are similar in shape yet the national region has a center of around 1,899 and is less spread out than the histogram for the Mid-Atlantic region. I can assume that all normal conditions have not been met. By gathering more data from the calculations of the test I will be able to better determine if indeed the normal conditions have been met or not. Hypothesis Test Calculations: Null Ho: U=1,944 H1: U= not= to 1,944 Level of Sig=0.05 Test Statistic= 15.45 P-Vaule= 2.72649E-44

Regional vs. National Housing Price Comparison Report 8 Interpretation: Since the P-value is less than the level of significance I will reject the null hypothesis that states the average square footage in the Mid-Atlantic region is equal to that of the average square footage in the National region. There is evidence that the average square footage in the Mid- Atlantic region is not equal to the average square footage in the National regions. Comparison of the Test Results: 95% Confidence Interval Alpha 0.05 confidence Interval= Sample mean +/- Margain of error Margin of error 4.38 Lower Bound 1,696.19 Upper Bound 1,704.95 I am 95% confident that the average square footage In the Mid-Atlantic is between [1,696.19, 1,704.95] Final Conclusions I was asked by the regional director to analyze two hypotheses (means). Doing so by determining if the initial hypothesis rose to be true or if the alternative showed more evidence that proved the null hypothesis to be false. In my findings, I was able to determine that the National region averages in both listing prices, as well as square footage, were significantly higher than those in the Mid-Atlantic. I rejected the null hypothesis in the one- tailed test because the alternative hypothesis provided more evidence of being true. I also rejected the null hypothesis in the two-tailed test because there was evidence that the null hypothesis was not equaled to the average square footage in the National regions. Running both the one-tailed and two-tailed tests I was able to address the answers to each of the regional directors’ questions in my report. I wasn’t surprised by the findings because a national region is more likely to have more data than my sample of 500. Also, other factors

Regional vs. National Housing Price Comparison Report 9 such as the locations, and what’s included with the homes can play a part in the overall national data region

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MAT 240 Project Two2

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