Hypothesis Testing for Regional Real Estate Company Assignment
Hypothesis Testing for Regional Real Estate Company Assignment
Introduction
There are a few different factors to consider when thinking about the listing price of a property. One is the size of the property in square footage. This will give an idea of how much space one has to work with and what potential buyers might be interested in. Another factor is the amenities that are included with the property. If there are special features or finishes that make it stand out, this can also affect the listing price. In general, expensive houses will have larger square footage and more luxurious amenities, while more modest homes may be smaller in size and include fewer high-end features. It is important to consult with a real estate professional to get an accurate estimate of what the house is worth before listing it on the market. The purpose of this assignment is to determine if the average cost per square foot of property in the Pacific region is less than $280 given the data collected under Pacific region.
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Setup
The population under consideration is price listing of 9,009 properties in all the ten regions. The overall mean of listing price is 288,407. To study this population, a sample size of 750 will be randomly selected from different counties within the Pacific region. A sample size of 750 from a population of 9009 would be representative of the population. A sample is a small portion of a population that is selected for study. In order to make generalizations about the entire population, the results from the study must be representative of the population. This can be done by randomly selecting participants from the population or by using a stratified sampling technique. A common method for calculating how large a sample size is needed is to use the confidence interval and margin of error. The margin of error tells us how confident we can be in our estimate of the population parameter. The larger the margin of error, the larger the sample size required.
Hypothesis
Null Hypothesis (H0)
The average cost per square foot in the Pacific region is not less than $280
Alternative Hypothesis (H1)
The average cost per square foot in the Pacific region is less than $280
To test the hypothesis, student two-tailed t-test will be used, the significance level is 0.05. A student t-test is used to compare the means of two groups. The test uses the t-distribution to calculate the probability that the difference between the group means is due to sampling error (in other words, that there is no real difference between the groups). If the probability is greater than 5%, then we can say that there is a statistically significant difference between the means of the two groups.
Data Analysis Preparations
There are a few things that were considered when determining an appropriate sample size for a population. The first is the size of the population itself. In this case, we are working with a population of 9009 individuals. Considering that sample sizes are usually representative of the entire population, it stands to reason that a larger population would require a larger sample size in order to be accurately represented. A sample size of 750 from a population of 9009 would be representative of the population. The sample size involves randomly selected price list of different properties from different counties within the Pacific region.
Table 1: Descriptive Statistics of the Sample
House listing price | |
Mean | 488523.6078 |
Median | 394220.5 |
Standard Deviation | 277084.4344 |
Count | 750 |
Table 1 shows the descriptive statistics for the variable under consideration (house listing price). The mean listing price is 488523.6078 with a standard deviation of 277084.4344. The sample size is 750 and the median is 394220.5
Graph 1: Histogram of the Sample
Graph 1 shows the histogram of the price listing variable from the sample. The graph shows that the data is skewed towards right (positively skewed). The distribution is similar to that of the population, meaning that sample is a representative to that of the population. T-test require the normality assumption i.e. the variable ought to be normally distributed (skewness is 0). Normality assumption has thus, been violated. However, this is not a problem because we are dealing with a large sample size greater than 20 i.e., 750. The tests will therefore be robust against such violations as a result of central limit theorem (Harrison et al., 2020). In other words, given large sample sizes, skewness is not a real problem for the statistical tests. The condition to perform t-test has been met.
Calculations
Using the test, =T.DIST.2T([test statistic], [degree of freedom]), the p-value obtained was 4.7708E-232 < 0.05
(Anderson, 2020)
t-statistics is 48.26
T.DIST.2T(48.26, 749)
p-value = 4.7708E-232
From the p-value, 4.7708E-232 < 0.05, we reject the null hypothesis and conclude that the average cost per square foot in the Pacific region is more than $280
Test Decision
From the p-value, 4.7708E-232 < 0.05, we reject the null hypothesis and conclude that the average cost per square foot in the Pacific region is less than $280.
There are a few different ways to approach this question, and the answer may vary depending on the specific circumstances. However, in general, one can reject the null hypothesis when the p-value is less than 0.05. This means that there is a 95% chance that the result is not due to chance or random fluctuations (Mertens & Recker, 2020). Therefore, if the researcher is trying to determine whether or not a difference between two groups is significant, and the p-value is less than 0.05, they can conclude that it probably is.
Conclusion
The test decision relates to the hypothesis; the one sample t-test is appropriate based on the data provided. Given the test statistics, one sample t-test will be appropriate. The conclusions are statistically significant. This means that there is a 95% chance that the result is not due to chance or random fluctuations. From the analysis, we reject the null hypothesis and conclude that the average cost per square foot in the Pacific region is less than $280. The salesperson should therefore approve the advertisement.
References
Anderson, S. F. (2020). Misinterpreting p: The discrepancy between p values and the probability the null hypothesis is true, the influence of multiple testing, and implications for the replication crisis. Psychological Methods, 25(5), 596. https://doi.org/10.1037/met0000248
Harrison, A. J., McErlain-Naylor, S. A., Bradshaw, E. J., Dai, B., Nunome, H., Hughes, G. T., … & Fong, D. T. (2020). Recommendations for statistical analysis involving null hypothesis significance testing. Sports biomechanics, 19(5), 561-568. https://doi.org/10.1080/14763141.2020.1782555
Mertens, W., & Recker, J. (2020). New guidelines for null hypothesis significance testing in hypothetico-deductive IS research. Journal of the Association for Information Systems, 21(4), 1. https://aisel.aisnet.org/jais/vol21/iss4/1/
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[Note: To complete this template, replace the bracketed text with your own content. Remove this note before you submit your outline.]
Hypothesis Testing for Regional Real Estate Company
[Your Name]
Southern New Hampshire University
Introduction
[Include in this section a brief overview, including the purpose of this analysis.]
Introduction
[Briefly describe how you generated your random sample of size 750.]
Setup
[Define your population parameter.]
[Write the null and alternative hypotheses.]
[Specify the name of the test you will use and identify whether it is a left-tailed, right-tailed, or two-tailed test.]
Data Analysis Preparations
[Describe the sample.]
[Provide the descriptive statistics of the sample.]
[Provide a histogram of the sample.]
[Specify whether the assumptions or conditions to perform your identified test have been met.]
[Identify the appropriate test statistic, then calculate the test statistic and identify your significance level.]
Calculations
[Calculate the p value using one of the following tests:
=T.DIST.RT([test statistic], [degree of freedom])
=T.DIST([test statistic], [degree of freedom])
=T.DIST.2T([test statistic], [degree of freedom])
Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size.]
[Use the normal curve graph as a reference to describe where the p value and test statistic would be placed.]
Test Decision
[Discuss how the p value relates to the significance level.]
[Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis.]
Conclusion
[Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.]
Module Five Assignment Guidelines and Rubric
Scenario
You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople just returned to the office with a newly designed advertisement. The average cost per square foot of home sales based on this advertisement is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280. In other words, he claims that the newly designed advertisement would result in higher average cost per square foot in the Pacific Region. He wants you to make sure he can make that statement before approving the use of the advertisement. In order to test his claim, you will generate a random sample size of 750 using data for the Pacific region and use this data to perform a hypothesis test.
Prompt
Generate a sample of size 750 using data for the Pacific region. Then, design a hypothesis test and interpret the results using significance level α = .05. You will work with this sample in the assignment. Briefly describe how you generated your random sample.
- Hypothesis Test Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test.
- Define your population parameter.
- Write the null and alternative hypotheses.
- Specify the name of the test you will use.
- Identify whether it is a left-tailed, right-tailed, or two-tailed test.
- Identify your significance level.
- Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and find the test statistic and significance level.
- Provide the descriptive statistics (sample size, mean, median, and standard deviation).
- Provide a histogram of your sample.
- Describe your sample by writing a sentence describing the shape, center, and spread of your sample.
- Determine whether the conditions to perform your identified test have been met.
- Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis.
- Calculate the sample mean and standard error.
- Determine the appropriate test statistic, then calculate the test statistic.
Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean (Pacific), and the target is 280. - Calculate the p value.
Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size.
Choose your test from the following:
=T.DIST.RT([test statistic], [degree of freedom])
=T.DIST([test statistic], [degree of freedom], 1)
=T.DIST.2T([test statistic], [degree of freedom]) - Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.
- Test Decision: Discuss the relationship between the p value and the significance level, including a comparison between the two, and decide to reject or fail to reject the null hypothesis.
- Discuss how the p value relates to the significance level.
- Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis.
- Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance.
- Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.
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