Hinchcliff_Megan_MAT_240_Project_Two

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Southern New Hampshire University *

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240

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Economics

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Feb 20, 2024

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docx

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Regional vs. National Housing Price Comparison Report 1 Report: Regional vs. National Housing Price Comparison Megan Hinchcliff Southern New Hampshire University
Regional vs. National Housing Price Comparison Report 2 Introduction Region : Mid-Atlantic Purpose This report aims to determine if the Mid-Atlantic region’s housing prices and square footage differ significantly from the national market. This report will answer the following three questions. First, are housing prices in the Mid-Atlantic region lower than the national market average? Second, is the square footage for homes in the Mid-Atlantic region different than the average square footage for homes in the national market? Third, for the Mid-Atlantic region, what is the range of values for the 95% confidence interval of square footage for homes? Sample To begin the analysis, a random sample of 500 homes was taken from the Mid-Atlantic region, which includes states, counties, listing prices, and square footage. To ensure the sample is random with minimal bias, an equation in excel was used. The sample was created by selecting the entire data set of homes from the Mid-Atlantic region and applying the =RAND() equation. Utilizing the copy-and-paste value feature in excel for the random sample column ensures that the calculation will not change throughout the analysis. The first 500 rows of data were then selected to represent the sample of homes in the region. Questions and type of test For this analysis, two hypotheses will be established. The first hypothesis is, are the average housing prices in the Mid-Atlantic region less than the average housing prices in the national market? The second hypothesis is, is the average square footage in the Mid-Atlantic region Not equal to the average square footage in the national market?
Regional vs. National Housing Price Comparison Report 3 A population parameter is a numerical value describing an aspect of an entire group or population. For the first hypothesis, the population parameter is the average house listing prices in the Mid-Atlantic region. The null hypothesis ( H 0 ) is a statement assumed to be true until sufficient data proves the statement to be false. In contrast, the alternative hypothesis ( H a ) contradicts the null hypothesis, which asserts that the true value of the population parameter is different from the hypothesized value. With the first hypothesis, the null hypothesis ( H 0 ) is that the average housing prices in the Mid-Atlantic region are equal to the average housing prices in the national market, which is $288,407. The alternative hypothesis is that the average housing prices in the Mid-Atlantic region are less than the average national market, which is $288,407. A left-tailed hypothesis test will be conducted to confirm or deny that the average listing price of the Mid-Atlantic is less than the national average. For the second hypothesis, the population parameter is the average square footage of homes in the Mid-Atlantic region. The null hypothesis ( H 0 ) is that the average square footage of homes in the Mid-Atlantic region is equal to the average square footage in the national market, which is 1,944. The alternative hypothesis is that the average square footage of homes in the Mid-Atlantic region is not equal to the average national market, which is 1,944. A two-tailed hypothesis test will be conducted to confirm or deny that the average square footage of the Mid-Atlantic is not equal to the national average. Level of confidence Estimation is the process of obtaining information about the population parameter that is both accurate and precise. Accuracy is measured in bias, whereas the standard error measures precision. A confidence interval indicates the probability that a population parameter will fall between a set of values a certain number of times. When an interval estimate is combined with a
Regional vs. National Housing Price Comparison Report 4 probability or hypothesis statement, it is called the confidence level. For this analysis, the confidence level is 95%, which means there is a 5% (significance level) chance of being incorrect. 1-Tail Test Population Parameter: The average house listing prices in the Mid-Atlantic region. Null Hypothesis: The average housing prices are equal to the average housing prices in the national market, which is $288,407. (µ = $288,407) Alternative Hypothesis: The average housing prices are less than the average national market, which is $288,407. (µ < $288,407) Significance Level: 0.05 or 5% Histogram of the Listing Price
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