7-3 Project Two Submission
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Southern New Hampshire University *
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240
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Mathematics
Date
Apr 3, 2024
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docx
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Uploaded by BrigadierResolve10210
DiAngeles Lino
MAT 240: Applied Statics Matthew Elwer
February 21,2024
7-3 Project Two Submission
Region:
I have decided to focus on the West South Central region for my report.
Purpose: This report's objective is to make a comparison between the listing price and square footage of the chosen region and the national listing price. Using the above data regarding the West South Central Region, we will use Excel to create a random sample of 500. “The housing prices in the West South Central region is lower than the housing prices in the National Market” is the first hypothesis, which is a left-tailed test. "The square footage for homes in the West South Central region is different than the average square footage for homes in the National Market" is the second hypothesis, which is tested using two tailed statistics.
Sample: The states from which the data is sourced, as well as the counties in each, are given in the sample. A few examples of these states are El Paso, TX; Acadia, LA; Harris, TX; Nacogdoches, TX; and Tulsa, OK. Along with listing the average cost per square foot, average housing costs, and average square footage of homes in those various counties, it also lists the region—West South Central.
Questions and type of test: "The housing prices in the West South Central region is lower than the housing prices in the National Market" is the first hypothesis, or h1, and it is a left-tailed test.
The second hypothesis, a two-tailed test, is that "the average square footage of homes in the National Market is not the same as the square footage of homes in the West South Central region." We will refer to the second hypothesis as h2. In addition to being the means of each hypothesis—which should be equal because they come from the same set of data—the population parameter for hypotheses h1 and h2 is also a random selection of fifty. The hypothesis for h1 is that West South Central house prices are less expensive than those in the National Market. The hypothesis for h2 is that the average square footage of homes in the National Market is different from that of homes in the West South Central region. A two-tailed hypothesis test is used for h2, whereas a left-tailed hypothesis test is used for h1. 1-Tail Test Hypothesis:
For a random sample of 500 listings, the sample mean is $230,359, whereas the national average listing price is $288,407. That the mean listing price is the same as the average listing price across the country is the null hypothesis. Alternatively, the mean listing price could be lower than the average listing price for the country. 0.05, or 5%, is the most significant level.
Data analysis:
Sample Standard Deviation
71983.45
Standard Error
3219.198
Sample Mean
$230,359
Sample Size
500
Median
$46,240
The mean, $230,359, is the center. It is widely dispersed and resembles a bell curve in many ways. With a tiny skew at the first quartile, it is more symmetric.
Hypothesis Test Calculations: There is -$18.03 in the test statistic.
It is 1E-56 for the p-value. Interpretation: The level of significance is exceeded by the p-value. The 1 is intended to be 56 places behind the decimal point, according to the p-value of 1E-56, and the level of significance is 0.05. As a result, the p-value is smaller than the significance level. The null hypothesis must be rejected since the p-value is less than the level of significance.
It has been observed that the West South Central region's average listing price is less than the national average.
Hypotheses: In terms of square footage, the national mean is 1,944, whereas the sample mean is 2,060. The assumption that the sample square footage mean, and the national average square footage are equal is known as the null hypothesis. The other possibility is that the sample mean of square footage differs from the average square footage of the country. Level of significance is 0.05.
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Data Analysis: Sample Mean
2,060
Sample Standard Deviation
309.236
Median
1,995
Quartile 1
1,848
Quartile 3
2217.625
Sample
500
The distribution graph and all the histograms were generated as best I could have done, however the resulting graph is extremely skewed. From the looks of it, point 3, 1,995 is where the middle is. Hypothesis Test Calculations:
The test statistic stands at 8.39. It must relocate 16 spaces behind the decimal point, according to the p-value of 4.938350E-16.
Interpretation: The p-value is significantly less than the significance level. (Connect the significance level and p value.)
We will have to reject the null hypothesis because the p-value is less than the level of significance. There is proof that the West South Central region's average square footage is less than the country's average square footage.
Comparison of the Test Results: By
calculating the alpha, we can get the confidence interval for the average square footage. Since we are looking for a 95% confidence interval, or 0.05, which is the same as our level of significance, the alpha is 1-0.95. The sample mean +/- margin of error formula is used to estimate the confidence interval. Then, we use the function =confidence.t (alpha, standard deviation, and sample size) to get our margin of error. For this data set, the result was 27.17. After that, we compute the lower and upper bounds by deducting
and adding the margin of error from the sample mean. 2087.23 is the upper bound and 2032.89 is
the lower bound. (Calculate the 95% confidence interval and provide an example or explanation of the computation process.)
The average square footage in the West South Central region is estimated to be between 2032.89 and 2087.23, with a 95% confidence level.
Final Conclusion
The West South Central region's average listing price is lower than the national average listing price, according to the statistics. Furthermore, there is a discrepancy between the West South Central region's average square footage and the national average.
Since the national averages data is bigger in scope, I was not shocked by the results.
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