Hypothesis Testing for Real Estate Advertising Impact

Hypothesis Testing for Regional Real Estate Company 1 Hypothesis Testing for Regional Real Estate Company Dianna Sheely Southern New Hampshire University

Hypothesis Testing for Regional Real Estate Company 2 Introduction The following report is created for the Regional Real Estate Company to analyze real estate data and its use in determining whether a regional salesperson should use a newly designed advertisement. The advertisement claims an average cost per square foot in home sales of $280. The salesperson claims that current sales are less than $280 per square foot and that this newly designed advertisement would result in a higher average cost per square foot in the Pacific region. Using a hypothesis test of 750 properties, we will analyze the data to determine if the claimed average cost per square foot is accurate and if this advertisement should be used. A random sample will be selected from the given data using the RAND function in excel. Once the data is randomized, data will be sorted, and the first 750 homes will be selected. Hypothesis Test Setup In this hypothesis test, the population parameter (μ) will be the Pacific region's mean cost per square foot. The null hypothesis (H 0 ) is m = 280. The alternative hypothesis (H a ) is m < 280. Since the alternative hypothesis (H a ) is less than our null hypothesis (H 0 ) parameter of 280 and our significance level is α = 0.05, we will test the sales persons claim using a left-tailed test. We use a left-tailed test when the alternative hypothesis states that the actual value of the parameter specified in the null hypothesis is less than the null hypothesis claims.

Hypothesis Testing for Regional Real Estate Company 3 Data Analysis Preparations Pacific Region Descriptive Statistics Sample Statistics Cost per square feet N 750 Mean $263.24 Median $200.92 Standard Deviation $158.64 Our histogram shows that the distribution for the Pacific region cost per square foot is skewed to the right, with the center at about $201 (median), with the majority of the listings falling between $165 to $226 per square foot. The following assumptions have been met to support the left-tailed t-test for means. The normal distribution has been met because we have a sample size of 750, which allows us to meet the Central Limit theorem. This theorem asserts that the sampling distribution of the mean will be

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Hypothesis Testing for Regional Real Estate Company 4 normally distributed if the sample size is large enough. The random condition has been met because we requested that we use 750 listings based on a random sample, which was calculated using the RAND function in Excel. And the alternative hypothesis (H a ), m < 280, is less than the null hypothesis (H 0 ) of m = 280. We were requested to use the significance level α = 0.05. Calculations Using Excel formulas, we have calculated the following: The sample mean (=Average) of Pacific Region cost per square foot is $263.24 Standard Deviation (=STDEV.S) of $158.64 . Our test statistic calculated as -2.893 t = 263.24 -280 158.64/√750 t = -2.893 Since we use a left-tailed t-test with our data, we will use the Excel formula =T.DIST([test statistic], [degree of freedom], 1) to calculate the p -value. Our sample returns a p -value of .00196. -5 -4 -3 -2 -1 0 1 2 3 4 5 t = -2.893

Hypothesis Testing for Regional Real Estate Company 5 Test Decision Comparing the p-value and significance level relationship helps us determine if the null hypothesis (H 0 ) is rejected or supported. With our p -value in our sample being .00196 and our significance level being α = 0.05, we see that .00196 < 0.05. Since our p -value is less than our significance level, we reject the null hypothesis and have convincing evidence that the average square foot for the Pacific region is less than $280 per square foot. Conclusion The hypothesis test was used to determine if the salesperson is correct in that the average cost per square foot currently being less than $280. The average cost per square foot in the Pacific region is lower, with a sample mean of $263.24; therefore, the salesperson is correct and should consider using the advertisement to boost sales.

MAT 240 Module Five Assignment

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