MAT 240 Module 5 Assignment

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Median Housing Price Prediction Model for D. M. Pan National Real Estate Company 1 Hypothesis Testing for Regional Real Estate Company Jessie Busch Southern New Hampshire University MAT 240: Applied Statistics Chuck Holbrook February 11, 2024

Hypothesis Testing for Regional Real Estate Company 2

Hypothesis Testing for Regional Real Estate Company 3 Introduction This analysis is designed to test a hypothesis in order to determine the validity of a claim made by a sales representative from Regional Real Estate Company regarding the Pacific region. The claim made by the sales representative regarding this hypothesis states that the typical cost per square foot in this particular region is less than $280. According to this sales rep, the cost per square foot may increase if it were to be advertised at $280. In order to provide approval for this advertisement, the Regional Real Estate Company needs to be shown that the information being provided is correct. To generate a random sample of 750 houses out of 1006 in the Pacific region, the formula =RAND() in Microsoft Excel. This randomly sorted the data from least to greatest. Then, I chose the first 750 samples from the data set and used them for the hypothesis testing; the other remaining samples were discarded. Hypothesis Test Setup In order to set up the population parameter for this test, we looked at whether the null hypothesis was equal to or greater than the hypothesized value or if it was not equal to or less than the hypothesis value. H 0 : μ = 280 H A : μ < 280 The analysis involved doing a left-tailed hypothesis test using t-distribution due to the unknown population standard deviation or p-value with a significance level of 0.05.

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Hypothesis Testing for Regional Real Estate Company 4 Data Analysis Preparations Sample Size 750 Sample Mean $266 Sample Median $201 Standard Deviation 164.974646 According to the initial data collected, the conditions necessary to conduct a left-tailed hypothesis test have been met. These conditions are proved to be random based on the formula that was used to generate the sample. Since one observation does not affect the other, it is considered independent. The sample is normal because the sample size is larger than 30, and no extreme outliers are detected. The results were interpreted using the hypothesis test with the significance level a = .05. Calculations Sample Mean $266 Sample Standard Error 6.02402232

Hypothesis Testing for Regional Real Estate Company 5 The T-Statistic was calculated by using the Microsoft Excel formula =(mean-target)/(standard error) for this data set. The mean is 266, the target is 280, and the standard error is 6.02. The actual formula is =(266-280)/(6.02). T-Statistic= -2.3255 The P-value was calculated by using a left-tailed hypothesis test using the formula =T.DIST(test statistic, sample size-1, Cumulative). For this date set, the test statistic is -2.3255, the sample size is 750 then subtract 1, and the cumulative is TRUE. The actual formula would look like =T.DIST(-2.3255,750-1,TRUE) P-Value= 0.01015354 Test Decision Using the left-tailed hypothesis test formula, it was determined that the p-value was 0.01015354, which is less than the level of significance of 0.05. If the p-value is less than or equal to the significance level, we reject the null hypothesis in favor of the alternative hypothesis. In this case, the p-value is less than the significance level; therefore, we reject the null hypothesis and

Hypothesis Testing for Regional Real Estate Company 6 accept the alternative hypothesis. This means that the claim, represented by the alternative hypothesis, is supported by the sample data. Conclusion The purpose of the study is to determine if the population mean (μ), representing the null hypothesis, is equal to 280 and, if the alternative hypothesis, the population mean is less than 280. The sales associate's claim was that the average cost per square foot for houses sold in the Pacific region was less than $280, but he wanted to have a new advertisement to state it was $280. He believed that advertising this information would boost sales prices and, in return, increase the average mean of $280. Based on the research, it was determined that the null hypothesis should be rejected due to the low p-value. Rejecting the null hypothesis suggests that the alternative hypothesis average cost per square foot for homes in the Pacific region is indeed less than $280. This supports the sales associate's claim that the Pacific region's average price per square foot is, in fact, lower than what is listed in the advertisement. However, it is important to note that this does not necessarily mean that advertising a mean cost of $280 will boost sales prices. This would require a further analysis with more information for the area.

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