MAT 240 Project Two Template

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Regional vs. National Housing Price Comparison Report 1 Report: Regional vs. National Housing Price Comparison Madison Jones Southern New Hampshire University

Regional vs. National Housing Price Comparison Report 2 Introduction Region : For the analysis the Mid-Atlantic region was used. Purpose : In this report a sample of 500 houses in the Mid-Atlantic region is taken to represent the real estate market in that region. Statistics are gathered through the random sample and compared against national real estate averages. Using statistical hypothesis testing this report aims to determine if the Mid-Atlantic region’s housing prices and housing square footage are significantly different from those of the national market. Sample: In the random sample used during this analysis 500 home sales were selected at random from the population of 1,001 in the Mid-Atlantic region. The Mid-Atlantic includes the states of New York, New Jersey, and Pennsylvania. The sample includes information for listing price, square feet, and price per square foot. Questions and type of test: The first variable being analyzed is listing price thus meaning the population parameter is the listing price of all home sales in the Mid-Atlantic region. My hypothesis is the average listing price of homes in the Mid-Atlantic region are less than the national average home listing prices. In the hypothesis the term less is used meaning the hypothesis test being completed will be a left- tailed test. The second variable being analyzed is square footage thus meaning the population parameter is the square footage of all home sales in the Mid-Atlantic region. My hypothesis is the average square footage of homes in the Mid-Atlantic region are different than the national average home square footage. In the hypothesis the term different is used meaning the hypothesis test being completed will be a two-tailed test.

Regional vs. National Housing Price Comparison Report 3 Level of confidence: In this analysis estimation and confidence intervals will be used to draw conclusions about the population parameters of listing price and square footage in the Mid- Atlantic region. In these hypothesis tests a 95% confidence level will be used meaning the statistics obtained in the hypothesis test are accurate with a 95% confidence. Also, in the two tailed test a confidence interval of 95% is used to estimate a range between where the true mean lies. The estimations done during this analysis can be used to help the real estate company make predictions about the house market in the Mid-Atlantic region. 1-Tail Test Population parameter: Listing price of all homes in the Mid-Atlantic region Null hypotheses (H0): The average listing price in the Mid-Atlantic region is equal to the average national listing price. (H0: U = $288,407) Alternative hypotheses (H1): The average listing price in the Mid-Atlantic region is less than the average national listing price. (H1: U < $288,407) Significance level: 0.05

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Regional vs. National Housing Price Comparison Report 4 Data analysis: Summary Statistics for Mid-Atlantic Region Listing Price Sample size 500 Mean $248,325 Median $189,975 Standard deviation 198444.5825 Quarter 1 $147837.50 Quarter 3 $276591.00 As depicted in the graph above the mean listing price is $248,325. This indicates that in the sample of 500 the average listing price of a home is $248,325. The median is also visibly represented in the above histogram. The histogram clearly shows that the majority of the sample fell within the first two bins ranging from $71,050 - $311,050 in price. Overall, 392 out of 500 data points lie within that range explaining why the median is $189,975. Based on the shape of the histogram it can be determined that the data is right skewed as the majority of data lies on the left side of the graph. Generally, the skewed data would indicate the assumption of normal

Regional vs. National Housing Price Comparison Report 5 condition would not be met. However, due to the large size of the sample and no major outliers being present normalcy can still be determined. Compared to the national statistics it is clear that the national listing price is higher than the sample mean listing price. By looking at the national listing price histogram some similarities can be seen between the data. For instance, the national listing price is also right skewed. Test statistic (t): -4.516 [Calculation (248,325-288,407)/ 8874.711525] P value: 0.000004 [Calculation =T.DIST(4.516,499,TRUE)] Interpretation: The P value is less than the significance level of 0.05. Thus, sufficient evidence exists to subject average listing price in the Mid-Atlantic is less than the National average. For this reason, the null hypotheses is rejected. Statistically this hypotheses test indicates the random sample of 500 home sales in the Mid-Atlantic region represents the population concluding that the average listing price in this region is less than national averages. 2-Tail Test Population parameter: Square footage of all homes in the Mid-Atlantic region Null hypotheses (H0): The average square footage in the Mid-Atlantic region is equal to the average national square footage. (H0: U = 1,944) Alternative hypotheses (H1): The average square footage in the Mid-Atlantic region is not equal to the average national square footage. (H1: U not equal 1,944) Significance level: 0.05

Regional vs. National Housing Price Comparison Report 6 Data Analysis: Summary Statistics for Mid-Atlantic Region Square Footage Sample size 500 Mean 1,690 Median 1,723 Standard deviation 329.0938702 Quarter 1 1550 Quarter 3 1869.25 As depicted in the graph above the mean square footage is 1,690. This indicates that in the sample of 500 the average square footage of a home is 1,690. The median is also visibly represented in the above histogram. The histogram clearly shows that the majority of the sample fell within the eighth and ninth bin ranging from 1,575- 1,935 in size. Overall, 251 out of 500 data points lie within that range explaining why the median is 1,723. Based on the shape of the histogram it can be determined that the data is symmetric as the data has a fairly even distribution through both sides of the histogram. No outliers are present, and the sample size

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Regional vs. National Housing Price Comparison Report 7 satisfies the assumption of normalcy. Thus, it can be determined that the data meets the qualification for normal conditions. Compared to the national statistics it is clear that the national square footage is higher than the sample mean square footage. By looking at the national listing price histogram some similarities can be seen between the data. For instance, the national square footage as appears to be symmetrical with the majority of its data lying within the middle two bins. Test statistic (t): -17.268 [Calculation (1,690-1,944)/ 14.71752529] P value: 0.0000 [Calculation =T.DIST.2T (-17.268,499)] Interpretation: The P value is less than the significance level of 0.05. Thus, sufficient evidence exists to subject average square footage in the Mid-Atlantic is not equal to the National average. For this reason, the null hypotheses is rejected. Statistically this hypotheses test indicates the random sample of 500 home sales in the Mid-Atlantic region represents the population concluding that the average square footage in this region is not equal to the national averages. Comparison of the Test Results: A 95% confidence interval provides a range of numbers with a 95% confidence that the true mean lies between the calculated range. For this calculation the equation is the margin of error + or – the sample mean. The margin of error can be found though the CONFIDENCE.T function in excel [=CONFIDENCE.T(0.05, 329.0938702,500)] margin of error equals 28.91595451. Then to calculate the confidence interval the equations are (28.91595451+1,690) making the upper bound equal to 1,718.77 and (28.91595451-1,690) making the lower bound equal to 1,660.94. Together the confidence interval is (1660.94,1718.77). In practicality the confidence interval indicates the true average square footage of homes in the Mid-Atlantic region lies between 1,660.94 and 1,718.77.

Regional vs. National Housing Price Comparison Report 8 Final Conclusions The purpose of this report was to draw statistical data from a random sample of 500 homes sold in the Mid-Atlantic region. The statistics would be used to complete two hypotheses test about the listing price and square footage of homes in the Mi-Atlantic and compare them to national averages. In the first hypothesis test a left-tailed test revealed significant evidence subjecting the Mid-Atlantic regions average listing price is less than the national average. Upon completing the second hypothesis test using a two-tailed test evidence subjected the mean square footage in the Mid-Atlantic region was not equal to that of the national average. With the statistical data from both these tests it was determined that both null hypotheses would be rejected. Using the results from both hypothesis tests the real estate company can use the data to make estimations about the Mid-Atlantic house market in relation to listing price and square footage. After reviewing all the data for this analysis, the findings were not surprising. From personal knowledge I would expect the Mid-Atlantic region to have generally lower home prices. When considering the region contains larger cities it also makes since that square footage is not equal to national averages because cities often have smaller homes with less square footage.

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