mat-240-project-two-completed
docx
keyboard_arrow_up
School
Harrisburg Area Community College *
*We aren’t endorsed by this school
Course
240
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
10
Uploaded by lrrossner
Downloaded by Leslie Rossner (lrrossner@gmail.com)
MAT 240 Project Two completed
Applied Statistics (Southern New Hampshire University)
Scan to open on Studocu
Studocu is not sponsored or endorsed by any college or university
Regional vs. National Housing Price Comparison Report
1
Downloaded by Leslie Rossner (lrrossner@gmail.com)
Report: Regional vs. National Housing Price Comparison
Kate Martin
Southern New Hampshire University
Regional vs. National Housing Price Comparison Report
2
Downloaded by Leslie Rossner (lrrossner@gmail.com)
Introduction
Purpose:
This report will examine two hypotheses related to the housing sales market. The study will utilize a sample data of 500 homes located within the New England region. The aim is to determine whether the housing prices in this region are higher than the national market average and to assess whether there are any differences in the average square footage of the homes in this region compared to the national market average.
Sample:
To obtain a random sample of 500 houses located within the New England region, we utilized the =rand() function within an Excel spreadsheet. The region consists of six states, namely Maine, New Hampshire, Vermont, Rhode Island, Connecticut, and Massachusetts. This method of sampling helps to ensure a true random sample, and we can continue to randomize the
sample to further enhance its randomness
Questions
and
type
of
test:
This report will conduct two different tests, both of which will utilize a significance level
of α = .05. The first test is a right-tailed test that focuses on the average listing price, with the following hypotheses:
Null
Hypothesis
(H0): The population mean (μ) of the listing prices is equal to 288,407.
Alternative
Hypothesis
(Ha): The population mean (μ) of the listing prices is greater than 288,407.
In simpler terms, the first test aims to determine whether the average listing price of the houses in the New England region is significantly greater than $288,407.
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
3
Downloaded by Leslie Rossner (lrrossner@gmail.com)
The second test in this report is a two-tailed test that focuses on the average square footage of the homes in the New England region, with the following hypotheses:
Null
Hypothesis
(H0)
: The population mean (μ) of the square footage is equal to 1,944, which is the average square footage of the national market.
Alternative
Hypothesis
(Ha)
: The population mean (μ) of the square footage is different than 1,944.
This test aims to determine whether there is a significant difference between the average square footage of the houses in the New England region and the national market average. To support this hypothesis, we will utilize estimation and confidence intervals to determine whether
there is evidence to reject or support the null hypothesis.
1-
Tail
Test
O
ur population parameter for this test is the mean listing price of homes for the entire population
of the New England region. Our null and alternative hypotheses are below, using the
significance level of α
=
0.05
(Null)H0:
μ
=
288,407
(Alternative)Ha:
μ
>
288,407
Regional vs. National Housing Price Comparison Report
4
Downloaded by Leslie Rossner (lrrossner@gmail.com)
Analysis:
Data
analysis:
Listing
Price
of
Homes
Mean
345836
Median
$330,050
Standard
Deviation
147378
Quartile
1
267838
Quartile
3
4277378
The chart above displays a right-skewed shape, which may occur when the mean is slightly higher than the median and in the direction of the skew. The graph’s range spans from around $150K to over $900K. Although similar in shape and direction to the national statistics graph, our data’s summary statistics are significantly higher. It is possible that outliers in our sample could be from areas where the housing market is more expensive than other regions. Our
significance level, α
=
0.05,
and sample size of 500 provide a normal distribution of data. With
Regional vs. National Housing Price Comparison Report
5
Downloaded by Leslie Rossner (lrrossner@gmail.com)
our random sampling, data distribution, and required sample size, the conditions for assessing our hypothesis have been met.
Hypothesis
Test
Calculations:
The formula used to calculate our test statistic very simply put is the (mean – target)/standard error. It looks like this for our equation: (345836-288407)/ (147378/). Which is 57429/6592= 8.71.
Next, we calculate the p
value using the T. DIST.RT function in Excel.
=T. DIST.RT([test statistic], [degree of freedom])
=T. DIST.RT([8.17], [500-1])
=0.000
Interpretation:
With our p value < α (0.05), we can reject the null hypothesis and conclude that the mean listing price in the New England region is greater than the mean listing price of the national market. The result is not surprising given that our sample data’s mean and median listing prices were already higher than the national market’s mean. Moreover, the scarcity of outliers in our data further supports our conclusion.
2-
Tail
Test
Hypotheses:
This test aims to determine whether the mean square footage of homes in the New England region is different from the mean of the National Market data. Therefore, the population parameter of interest is the mean square footage of homes for the entire population of
the New England region.
First, we identify our null and alternative hypotheses below. Again, we are using the
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
6
Downloaded by Leslie Rossner (lrrossner@gmail.com)
significance level of a=0.05
(Null)
H0:
μ
=
1944
(Alternative)Ha:
μ
≠1944
Data
Analysis:
Square
Footage
of
Homes
Mean
1870
Median
1,875
Standard
Deviation
262
Quartile
1
1757
Quartile
3
2053
Data
Analysis:
The chart above is more symmetrical, with a few outliers on the right side. The center of the graph falls between 1,800 and 2,000 sqft, and the overall range is from 1,200 to just over 3,000sqft. Although slightly smaller in range than the national graph, the shape and symmetry are similar, and the summary statistics from our data are comparable to the national summary
Regional vs. National Housing Price Comparison Report
7
Downloaded by Leslie Rossner (lrrossner@gmail.com)
statistics. This leads us to conclude that our null hypothesis calculation is accurate, and the
average square footage of homes in our region is not significantly different from that of
the national market.
As mentioned in our right tailed test, some of the potential outliers in our sample may
come from areas where the housing market is more expensive than in other regions. This is
expected given that our region encompasses vast counties, some with more available land than others. Our significance level remains as a=0.05, and we used a sample size of 500 which provided us with a normal distribution of data. Our random sampling, data distribution
and sample size again met the overall conditions for testing our hypothesis.
Hypothesis
Test
Calculations:
We again need to determine the test statistic. The formula for calculating the test statistic is the (mean – target)/standard error. So, in our case it would be = (1870-1944)/ 262/). =- 74/11.724=-6.31
Again, the next step is to calculate for our p value. This time the formula function in Excel will be T.DIST.2T.
=T.DIST.2T ([-6.31], [500-1])
=0.00000
Interpretation:
Based on the above information, the p-value is exceedingly small (0.000000), which is less than our significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is evidence suggesting that the average square footage in the New England region is different from the national average square footage. In other words, the alternative hypothesis that the population mean is not equal to 1,944 sqft is supported, while the null hypothesis that the
Regional vs. National Housing Price Comparison Report
8
Downloaded by Leslie Rossner (lrrossner@gmail.com)
population mean is less than or equal to 1,944 sqft is rejected.
Comparison
of
the
Test
Results:
To calculate the 95% confidence interval, we first need to identify the margin of error using Excel. The formula is =CONFIDENCE.T(alpha, standard deviation, sample
size).
Margin error=CONFIDENCE.T(0.05,262,500
Margin error=23.02
The confidence interval is the range of values that fall below and go above the New England region square footage mean. Now that we have the margin error of 23.02, we take
that number and both add and subtract it from the New England square footage mean. In doing so, we produce the lower bound amount of 1847 and the upper bound amount of 1893.
To wrap up, we can say that we are 95% sure that the square footage in the New England region will fall within the ranges of 1847 and 1893 sq ft.
Final
Conclusions
In general, our findings from the sample data we collected were what was
anticipated. We focused on the New England region because we knew that typically the real estate market in this area tends to be more expensive than in other regions. Our initial right tailed test confirmed this for us. In our two tailed test, we were able to determine that although the price of homes in this region may be higher than the national average, the average square footage of homes is not remarkably similar to those in the rest of the country. It gives us information that questions how closely the square footage of a house is related to the price. More samples and testing would need to be done to further our conclusions and research. Overall, the
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
9
Downloaded by Leslie Rossner (lrrossner@gmail.com)
results were not particularly surprising.