Hypothesis Testing in Real Estate: Analyzing Cost per Square Foot

Hypothesis Testing for Regional Real Estate Company 1 Hypothesis Testing for Regional Real Estate Company Desiree McKenzie Southern New Hampshire University

Hypothesis Testing for Regional Real Estate Company 2 Introduction I have been hired by the Regional Real Estate Company to help analyze cost per square foot data that has been collected from home sales throughout the Pacific region to determine if a newly designed advertisement should be approved. The new ad states that the average cost per square foot of a home in the Pacific region is $280 and advertising the information could help attract more customers. However, a salesperson within the company claims that the average cost per square foot in the Pacific region is actually less than $280. Before approving, the company would like to test the accuracy of their statement before releasing the information to their customer base to avoid false advertisements. For this analysis, I was able to generate a random sample of 750 homes from the Pacific region by isolating the Pacific region data in Excel and adding a random number to the end of each row using the =Rand() function. From the 1,001 homes listed in the Pacific region dataset, I selected and sorted the data by their random numbers from smallest to largest, then used the first 750 homes as the sample size I needed for the hypothesis testing and deleted the remaining data. Hypothesis Test Setup The population parameter for this hypothesis test is the mean dollars per square foot of homes in the Pacific region. I am using a t-test for this analysis where the null hypothesis is Ho=280 and the alternative hypothesis is Ha<280. The alternative hypothesis helps to identify the tail of the test and in this case, Ha is claiming the mean to be less than 280, making this a left-tailed test. Data Analysis Preparations The sample data of 750 homes from the Pacific region yielded the following descriptive statistics for the analysis (Figure 1) and I’ve included a histogram to better depict the spread of the sample (Figure 2):

Hypothesis Testing for Regional Real Estate Company 3 Figure 1 – Figure 2 – The assumptions to perform this t-test analysis have been met because it is a truly random sample and there are more than 30 values being tested. The histogram, in Figure 2, shows a spread of $104 - $1,071 per square foot with a center of $263.34 per square foot and an overall right-skewed shape, meaning most of the homes have a cost per square foot between $104 - $253. There is also a significance level of 0.05 allowing for 5% error, which can occur because

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Hypothesis Testing for Regional Real Estate Company 4 the sample of 750 homes was taken from a list of 1,001 homes from the Pacific region and was not pulled from the total population of the Pacific region. Calculations The sample mean is $263.34, the sample standard deviation is $163.30, and the standard error of the sample is $5.96, all of which were calculated and provided in Figure 1. With these values, and remembering that we’re trying to determine if cost per square foot is less than the target cost of $280, we can determine the appropriate test statistic with the equation (mean – target)/standard error. Test statistic = (263.34-280)/5.96 = -$2.79. With the test statistic determined to be -$2.79, I was able to use the Excel function =T.DIST([test statistic], [degree of freedom], 1) to calculate the p-value, which will be the probability that Ho (mean < $280) is true. p-value = T.DIST(-$2.79, 749, 1) = 0.00267485 Figure 3 – Using a normal curve graph as reference, the p-value would be placed 2.79 standard deviations to the left, below the mean (the mean is 0 on the normal curve graph in Figure 3) and the p-value would be a shaded area to the left of the test statistic to correspond to the probability of 0.00267485.

Hypothesis Testing for Regional Real Estate Company 5 Test Decision If we compare the relationship of the p-value 0.00267 to the significance level of 0.0500 we can determine that the p value is less than the significance level. For this hypothesis test, the p value is less than the significance level, so we will reject Ho ( the null hypothesis), there is sufficient evidence to support the claim that the mean cost per square foot of a home in the Pacific region is less than $280. Conclusion Regional Real Estate Company hired me to conduct an analysis and hypothesize whether a salesperson’s claim that the average cost per square foot for a home in the Pacific region was less than a targeted cost of $280 per square foot. The test concluded that the Pacific region has a cost per square foot that is less than $280, making the salesperson’s claim valid and the advertisement could be approved. The company’s salespeople are selling homes for more dollars per square foot and getting more money per square foot for their clients, however, the analysis does only represent 750 of the 1,001 homes listed in the dataset from the Pacific region. Therefore, this analysis does not provide an accurate representation of the entire population for the cost per square foot of homes in the Pacific region.

MAT 240 Module Five Assignment - D.McKenzie 100123

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