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Regional vs. National Housing Price Comparison Report

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Report: Regional vs. National Housing Price Comparison Noah Omar Southern New Hampshire University

Regional vs. National Housing Price Comparison Report

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Introduction Purpose: In this report we will be looking at two hypotheses about the house sales market. We will be using a sample data of 100 within the New England region. We will be looking to see if the housing prices in our region is higher than the national market average, as well as looking to see if the square footage of the homes in our region differs than the average square foot of the national market. Sample: Below is random sample. Included in our sample data is the state, county, region, house listing price, and square footage of the listing. State

County

Region

House listing price

Square footage

CT NH ME

Fairfield Merrimack Androscoggi

New England New England New England

$842,050 $297,050 $189,050

2,857 2,150 1,707

NH CT NH VT MA ME ME CT MA VT MA VT NH CT MA ME CT CT MA

n Hillsborough Hartford Belknap Windsor Plymouth Kennebec Cumberland Windham Norfolk Rutland Middlesex Rutland Merrimack Fairfield Suffolk Kennebec Fairfield Fairfield Plymouth

New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England

$375,050 $259,950 $292,550 $274,050 $502,807 $215,050 $369,407 $250,000 $615,045 $199,950 $655,000 $198,300 $307,050 $739,050 $754,500 $166,300 $744,050 $749,050 $477,050

2,157 1,691 1,867 1,922 2,022 1,740 1,823 1,706 2,282 1,857 2,400 1,809 2,201 2,919 1,361 1,631 2,689 2,946 2,016

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CT ME

Middlesex Androscoggi

New England New England

$340,000 $215,050

2,012 1,706

RI NH MA MA CT ME NH CT NH MA MA NH NH MA RI ME MA MA RI MA NH MA NH NH CT ME CT MA NH CT MA MA MA VT RI NH NH MA CT ME VT

n Providence Hillsborough Hampshire Berkshire Middlesex Penobscot Rockingham Middlesex Rockingham Essex Middlesex Grafton Merrimack Bristol Newport York Berkshire Franklin Providence Essex Grafton Essex Merrimack Merrimack Litchfield York Middlesex Norfolk Grafton Windham Hamden Hamden Hamden Rutland Newport Belknap Grafton Worcester New London Kennebec Franklin

New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England

$259,500 $362,450 $325,050 $379,050 $339,950 $149,050 $458,521 $333,950 $429,950 $574,950 $669,950 $229,050 $283,525 $418,750 $600,000 $339,950 $387,050 $280,000 $259,950 $550,000 $267,050 $515,393 $329,000 $347,000 $330,050 $338,550 $325,050 $635,050 $222,450 $215,950 $239,950 $197,050 $239,950 $235,050 $549,050 $299,950 $232,500 $319,950 $279,950 $199,950 $219,950

1,500 2,147 1,907 2,010 1,993 1,563 2,033 1,812 2,066 2,110 2,222 1,743 2,002 1,900 2,079 1,768 2,016 1,928 1,512 2,131 1,798 2,027 2,145 2,162 1,882 1,792 1,260 2,240 1,700 1,632 1,695 1,561 1,674 1,919 2,034 1,792 1,752 1,881 1,570 1,715 1,750

Regional vs. National Housing Price Comparison Report ME CT RI MA MA RI MA CT NH CT ME CT CT CT MA NH ME NH MA CT MA MA VT NH NH MA RI MA ME RI CT MA MA ME CT

Penobscot New Haven Bristol Suffolk Franklin Bristol Barnstable Hartford Cheshire Litchfield York Fairfield New London Wind Ham Worcester Strafford Kennebec Belknap Middlesex Hartford Berkshire Hamden Windsor Merrimack Hillsborough Norfolk Kent Hamden Kennebec Providence Wind Ham Norfolk Berkshire Kennebec Fairfield

New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England New England

Questions and type of test:

$154,950 $269,950 $485,000 $739,050 $250,000 $499,950 $575,050 $249,050 $260,050 $342,450 $345,050 $754,500 $289,950 $259,050 $369,950 $310,664 $185,050 $299,950 $627,050 $247,750 $360,050 $224,950 $335,050 $322,500 $334,950 $599,500 $275,000 $250,050 $212,050 $269,950 $251,050 $627,050 $388,886 $215,050 $829,950

4 1,600 1,599 2,009 1,336 1,899 2,234 1,890 1,504 1,841 2,103 1,772 2,774 1,850 1,634 1,983 1,843 1,704 1,803 2,329 1,452 2,061 1,595 2,158 2,095 2,124 2,274 1,515 1,729 1,790 1,500 1,601 2,169 2,017 1,760 2,867

Regional vs. National Housing Price Comparison Report We will be conducting two different tests in this report. For both these tests we will be using a significance level of α = .05

The first test will be a Right Tailed Test, focused on the average listing price, with a hypothesis of: H0: μ = 288,407 Ha: μ > 288,407 In this Right Tailed Test, we are trying to see if there is enough statistical evidence to see if the average price of homes in our selected region is greater than the national market average.

The second test will be a Two Tailed Test, focused on the average square footage, with a hypothesis of: H0: μ = 1,944 Ha: μ ≠ 1,944 For this test we will see if the average square footage of the homes in our region is different than the average for the national market. We will be using estimation and confidence intervals to support our test our theory and see if the is evidence to reject or support our hypothesis.

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Regional vs. National Housing Price Comparison Report 1-Tail Test Hypothesis: The information being gathered is to determine if mean listing price of the New England region is greater than the mean of the National Market data. Thus, our population parameter is the mean listing price of homes for the entire population of the New England region. Since we are working with only a portion of the sample data the population parameter remains unknown. Our null and alternative hypotheses are stated below: H0: μ = 288,407 Ha: μ > 288,407

Data analysis:

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Descriptive Statistics Listing Price of Homes Mean Quartile 1 Median Quartile 3 Standard Deviation Sample Size

$372,073.97 $250,000.00 $323,775.00 $444,235.71 $172,408.10 100

The shape of the above chart is skewed to the right. This can occur due to the mean being slightly higher than the median, with the mean being in the direction of the skew. The spread on this graph ranges from approximately $150k to a little over $900k. In relation to the national statistics graph it is similar in shape and direction it is skewed towards, however the summary statistics from our data is significantly greater than the national summary statistics. Possible outliers in our sample might come from areas where the housing market is relatively more expensive than other areas in the region. Again, our significance level is denoted as α = 0.05 and we utilize a sample size of 100, which provides us with relative normal data distribution. Overall, our conditions to test our hypothesis have been met with our random sampling, our data distribution, and the required size of our sample.

Hypothesis Test Calculations: We use the following formula to determine our test statistic: T Test = (x – μ) / (σ / √n) = (372,073.97 – 288,407) / (172,408.10 / √100) = 4.85 To calculate our p value we use the T.DIST.RT function in Excel

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=T.DIST.RT([test statistic], [degree of freedom]) The degree of freedom is calculated by subtracting 1 from the sample size. =T.DIST.RT([4.85], [100-1]) P value = 2.27E-06 In relation, our p value < α

Interpretation: Since our p value is greatly less than our significance level of 0.05 we can reject the null hypothesis and conclude that there is enough data to support that the mean listing price in the New England region is greater than the mean listing price of the national market. This conclusion was to be expected since the mean and the median listing price of our sample data was already well above the mean of the national market. Also, the fact that there were not many outliers present within our data further proves this.

2-Tail Test Hypotheses: The information being gathered for this test is to determine if mean square footage of homes in the New England region is different than the mean of the National Market data. Thus, our population parameter is the mean square foot of homes for the entire population of the New England region. Again, since we are only working with only a portion of the sample data the population parameter remains unknown. Our null and alternative hypotheses are stated below: H0: μ = 1,944 Ha: μ ≠ 1,944

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Data Analysis:

Descriptive Statistics Square Footage of Homes Mean Quartile 1 Median Quartile 3 Standard Deviation Sample Size

1,923 1,706 1,881 2,087 332.38 100

The shape of this chart is more symmetric, with a few outliers on the right side. The center of the graph falls within the 1,700 sqft to 2,000 sqft. The overall range of the graph is from 1,200 sqft to a little over 3,000 sqft. In relation to the national statistics graph it is similar in shape and symmetry, the range is slightly smaller compared to the national graph however the center of the spread stays relatively the same. The summary statistics from our data is also comparable to the national summary statistics. This leads us to believe that our null hypothesis

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calculation is accurate in that the average square foot of homes in our region is not so different than that of the national market. As state in our right tailed test, some of the possible outliers in our sample might come from areas where the housing market is relatively more expensive than other areas in the region. This is also to be suspected since our region covers vast county, some with more land available than others. Again, our significance level is denoted as α = 0.05 and we utilize a sample size of 100, which provides us with relative normal data distribution. As before the overall conditions to test our hypothesis have been met with our random sampling, our data distribution, and the required size of our sample.

Hypothesis Test Calculations: We use the following formula to determine our test statistic: T Test = (x – μ) / (σ / √n) = (1923 – 1,944) / (332.38 / √100) = -0.63 To calculate our p value, we use the T.DIST.2T function in Excel =T.DIST.2T([test statistic], [degree of freedom]) =T.DIST.2T([-0.63], [100-1]) P value = 0.53 In relation, our p value > α Interpretation: Since our p value is greatly more than our significance level of 0.05 we fail to reject the null hypothesis and conclude that there is not enough data to support that the mean square

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footage in the New England region differs from mean square footage of the national market. Again, this conclusion was to be expected since the summary statistics of our sample data was extremely similar to that of the national market. Comparison of the Test Results: To calculate our confidence interval, we need to first determine our margin of error. We do this using the function m = z*(σ/√n) = 1.96(332.38/√100) = 1.96(33.238) = 65.15 ≈ 65 Using our margin of error, we determine our lower bound and upper bound by subtracting and adding the margin of error to our sample mean. Lower bound = x - m = 1923 – 65 = 1858 Upper bound = x + m = 1923 + 65 = 1988 With this result we can say that we are 95% confident that the average square foot for houses in the New England region falls within the range of [1858, 1988]. Since the national market mean of 1944 falls within that range, this would be further proof to not reject the null hypothesis.

Final Conclusions Overall, the findings for the sample data we selected was to be expected. We select the New England region because it was a region where the real estate market is generally more

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expensive. From our initial right tailed test and our sample data this proved to be correct. Also, in our second 2 tailed test we were able to determine that although the price of the homes maybe higher than the national data the average square footage of homes remains the same. This leads us to conclude that although the square footage of a house is directly correlated to the price of the house, the average square footage of the homes bought remains relatively the same throughout the nation. From this we can continue to start guessing on things such as the pay rate and cost of living between different regions and how it correlates to the type of homes people are looking to purchase. Ultimately, the findings from our data was to be expected but still very insightful....