MAT 240 Project Two Template finale

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Feb 20, 2024

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Regional vs. National Housing Price Comparison Report 1 Report: Regional vs. National Housing Price Comparison Kelli Usher Southern New Hampshire University

Regional vs. National Housing Price Comparison Report 2 Introduction Region : East North Central is the region I picked for this report. Purpose : The purpose of this report is to tell the Real Estate Company that has hired me if the prices are higher or lower than the national average cost and compare the square footage to the national average in the cost of the homes. Sample: My sample comes from a data sheet for the region I picked which is the East North Central. I picked 500 random counties for the analysis I will be doing today. These are picked randomly by just selecting the first 500 on the data sheet. This sample includes the states of WI, IN MI, IL, OH, multiple counties in each state, the listing sale price the cost per square foot and the square footage per house. Questions and type of test: Here are the questions I will be helping to answer in this report. Are housing prices in your regional market lower than the national market average? Is the square footage for homes in your region different than the average square footage for homes in the national market? For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market? I will be using the 1 tailed and the 2 tailed testing equations. Both can be used in this scenario because there are more than 30 variables. First hypothesis: The population parameter for these questions is the average price in the East Central region which consists of $195,632. This is $92,775 lower than the nation’s average. First hypothesis: In this hypothesis I will test the theory that houses are more or less expensive in the East North Central region that I have chosen. This testing also will include the square footage of the houses in this area to see if they are the same, more or less than the average

Regional vs. National Housing Price Comparison Report 3 square footage to the national average. We will also be able to tell if the price per square foot is more or less than the average square footage cost of the national average. First hypothesis: I will be using the 1 tailed test in this hypothesis test. This hypothesis test will help show the average, and the standard deviation. Second hypothesis : I will be using the 2 tailed test in this hypothesis test. This hypothesis test will help show more information in the testing process than the 1 tailed test. Describe the population parameter for the variable you are analyzing. Second hypothesis: In my second hypothesis test I will be looking for the answer to the question is my region higher or lower priced than the national average. Second hypothesis: In my second test I will be using a 2 tailed (right tail). Level of confidence: [Estimating the cost of the houses in my area are represented by the 500 random houses I have chosen I will first have to make sure and average them out to compare to the average cost of the national data I have been given to use. I will complete this test and have a 95% confidence level that my average is accurate for the new data that is needed for the company that has hired me. 1-Tail Test Hypothesis: The population parameter I am using is the random 500 house prices and their average compared to the national average of house prices. Hypothesis: [H0: u=$288,407 which is the national average provided by the National Summary Statistics and Graphs House Listing Price by Region PDF. This hypothesis is used when the answer is equal to the average. H1: u<$288,407 this is when the average is lower than the average.

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Regional vs. National Housing Price Comparison Report 4 Note : For means, define a hypothesis that is less than the population parameter. Hypothesis: The significance level I will be using is 5% or 0.05. This will help give a normal with less space for error. Data analysis: I did do another histogram BUT could not get it to transfer. Data analysis: [In a table, provide summary statistics including sample size, mean, median, and standard deviation. Data analysis: [Summarize your sample data, describing the center, spread, and shape in comparison to the national information (Under “Supporting Materials,” see the National Summary Statistics and Graphs House Listing Price by Region PDF in the learning management system). Note : For shape, think about the distribution: skewed or symmetric.] Data analysis: [Check the assumptions by determining if the normal condition has been met. Determine if there are any other conditions that you should check and whether they have been met. Note : Think about the central limit theorem and sampling methods.] Hypothesis Test Calculations: [Determine the appropriate test statistic ( t ). Note : This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.] Hypothesis Test Calculations: [Calculate the probability ( p value). Note : This calculation is done with the T.DIST function in Excel: =T.DIST([test statistic], [degree of freedom], True). The degree of freedom is calculated by subtracting 1 from your sample size.] Interpretation: In this testing I have determined that the national average is higher than the regional average for the area I picked to do y report on. The p-value is higher than the

Regional vs. National Housing Price Comparison Report 5 significance level I choose to have as my level of providing the information I am using to give my final decision on. Interpretation: In my report I will say fail to reject based on the information I have found. Interpretation: In the testing process of the data, I have used I interpret the results as being in the favor of saying the national average is higher than the that of the region I picked. The national average is $288,407 which is found to be $92,775 higher than the East North Central area I have processed in my testing. 2-Tail Test Hypotheses: I will be using hypothesis test 2 tailed for the next question. This next question refers to the square footage average of my region compared to the national square footage as reported on the data sheet I am getting my information from. Hypotheses: [Write null and alternative hypotheses. Note : For means, define a hypothesis that is not equal to the population parameter.] Hypotheses: My significance level will also be 0.05 on this test as well. Data Analysis: I can not get the histogram to transfer to this paper BUT it is done and on the other attachment. Data Analysis: [In a table, provide summary statistics including sample size, mean, and standard deviation. Data Analysis: [Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note : For shape, think about the distribution: skewed or symmetric.]

Regional vs. National Housing Price Comparison Report 6 Data Analysis: [Check the assumptions by determining if the normal condition has been met. Determine if there are any other conditions that you should check and whether they have been met. Note : Think about the central limit theorem and sampling methods.] Hypothesis Test Calculations: [Determine the appropriate test statistic ( t ). Note : This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.] Hypothesis Test Calculations: [Calculate the probability ( p value). Note : This calculation is done with the TDIST.2T function in Excel: =T.DIST.2T([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.] Interpretation: [Relate the p value and significance level.] Interpretation: [Make the correct decision (reject or fail to reject).] Interpretation: [Provide a conclusion in context to your hypothesis.] Comparison of the Test Results: [Calculate and report the 95% confidence interval. Show or describe the method of calculation.] Final Conclusions Summarize Your Findings: To summarize my findings, I would start by saying the national average for cost and square foot is not accurate for the whole nation. It may be in some parts but you need to look at listings in the area you are wanting to purchase and get your average for that area only. When I look at the national average it indicates to me, I should be paying $92,775 more for a house. I know this is just one area but how many areas are thrown off by this average cost that may or may not be right for that area.

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Regional vs. National Housing Price Comparison Report 7 Discuss : Yes, I was surprised by the findings because I looked the prices over and thought for sure it was going to be way higher than the national average. So, when the equations had worked out to show this region was actually lower than the national average I was surprised.

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