MAT 240 Project Two
docx
keyboard_arrow_up
School
Southern New Hampshire University *
*We aren’t endorsed by this school
Course
240
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
6
Uploaded by GrandChimpanzeePerson1081
Regional vs. National Housing Price Comparison Report
1
Report: Regional vs. National Housing Price Comparison Melanie Maxwell
MAT-240 Applied Statistics
Dr. Reel
Southern New Hampshire University
Regional vs. National Housing Price Comparison Report
2
Introduction
Region
: For intents and purposes of this analysis I have selected the West South Central Region.
Purpose
: The purpose of this report is to determine if the West South Central regions pricing and
square footage is significantly different from the National Market. To begin our investigation
we will be using two different hypothesis tests that will provide statistical evidence to support our claims.
Sample: I began my analysis by collecting a random sample of 500 properties in various counties, using the =RAND() function in excel. This generated a true random selection so that I could begin testing.
Questions and type of test: For my selected sample in the West South Central Region we will begin by answering the following two questions: 1.
Are housing prices in your regional market lower than the national market average?
2.
Is the square footage for homes in your region different than the average square footage for homes in the National Market? First we will conduct a 1-tailed test (left), which will show if the sample mean is higher or lower than the population mean and provide us with direction. We will determine if the average housing prices in our region is less than the National Market. Followed by a 2-
tailed test, which will show if our values are less than the average of the market. Which will see if one average is different than the National average.
1-Tail Test
The population parameter for this test will be the pricing of our properties in the West South Central region. The null hypothesis is that the mean listing price in West South Central is
Regional vs. National Housing Price Comparison Report
3
equal to the National average of $288,407. The alternative hypothesis is that the mean is less than the National average $288407. We will be using 5% or 0.05 as the level of significance for these tests. Data Analysis
National Average Listing Price
$288,407
Sample Mean
$224,396
Sample Standard Deviation
71253.03388
Standard Error
3186.532547
From our sample of 500 properties, we concluded the following. The sample mean is $224,396, the median listing price is $224,339 and the standard deviation is 71253.03. Our graph is slightly skewed right, but also appears to be a bit evenly distributed. There are a few outliers on the graph that caused a difference in our numbers.
Hypothesis Test Calculations
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Regional vs. National Housing Price Comparison Report
4
We gathered this information by calculating the test statistic using the formula =(224396-
288407)/3186.532, which resulted in a negative number -20.0878. Hypothesis Test Calculations
Next, we calculated our p-value. Using the T.DIST function in Excel: =T.DIST([-20.0878], [499],1). Our sample mean is statistically significantly lower than the national average. Since the p-value is higher than the level of significance we will fail to reject the null hypothesis. Because we have failed to reject there is evidence that the average listing price of West South Central is higher than the National average listing price. 2-Tail Test
Hypotheses:
We have moved forward to our two tailed test. In this test we will determine if the average square footage is different than the square footage of the National Market. The mean square footage for the National Market is 1,944 square feet. Our level of significance is 0.05.
Hypotheses:
Since the p-value is higher than the level of significance we will fail to reject the null hypothesis. There is evidence that the average square footage in the West South Central
region is not equal to the national markets average.
Regional vs. National Housing Price Comparison Report
5
Data Analysis:
Data Analysis
National Market square footage
1944
Sample Mean
2,039
Sample Standard Deviation
295.5188074
Standard error
13.21600284
Regional vs. National Housing Price Comparison Report
6
Data Analysis:
For our sample of 500 properties we concluded the following information regarding the average square footage of the West South Central region. The sample mean is 2039, as opposed to the national markets sample mean of 1944. The median square footage is 1982, as opposed to the national markets median of 1899. The standard deviation is around 296, as opposed to the national markets standard deviation of 385. Just as with the listing price graph, our graph is almost exactly evenly distributed.
Hypothesis Test Calculations:
We gathered this information by calculating the test statistic in excel. We used the formula =(2039-1944)/13.21600284=7.16831176. Our test statistic is 7.1683176.
Hypothesis Test Calculations:
Our p-value was generated using the T.DIST formula. Upon entering this information in our data spreadsheet we yielded =T.DIST.2T([7.16831176,499])= 2.75
Comparison of the Test Results: From our data collection, we gathered
that there is a margin of
error of about 25.97, with an upper bound of 2065 and a lower bound of 2013. From this information we can assure you that we are 95% confident that the average square footage in the West South Central region is between 2013 and 2065.
Final Conclusions
To conclude this report we have found that the pricing of the West South Central region is significantly higher than the pricing in the National Market. This can be attributed to a number of things as, the square footage has also played a major role, as it is significantly higher as well. The location may also play a factor. I was not surprised by the results as higher square footage, should yield a higher listing price.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help