MAT 240 Module Five Assignment

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Feb 20, 2024

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Hypothesis Testing for Regional Real Estate Company 1 Hypothesis Testing for Regional Real Estate Company Joshua D. King Southern New Hampshire University

Hypothesis Testing for Regional Real Estate Company 2 Introduction The purpose of this analysis is to determine if the advertisement of the average cost per square foot of home sales in the Pacific region of $280 is a valid statement based upon data from home sales in the region. To obtain a completely random sample, a blank column was given the header name “Random”. Under this header, a random number was assigned to the first row using the Excel function, =rand( ). After assigning a random number to the first row, a random number was assigned to all rows of data by double clicking the bottom right-hand corner of the first random number. All data in the spreadsheet was then selected with Ctr-A. With all data selected, the Data tab within Excel was used to access the sort function. After selecting the sort function, parameters were set to sort the random column from smallest to largest, while making sure to check the contained header box and then selecting okay. With the data sorted, all data that fell below row 752 was removed and the spreadsheet contained 750 randomly obtained samples. Hypothesis Test Setup The population parameter that is defined within the model is the mean cost per square foot in the Pacific region. The null hypothesis is that the average cost of square footage of homes in the Pacific region is equal to $280.00. The alternative hypothesis is that the average cost of square footage of homes in the Pacific region is less than $280.00. The name of the test that will be used to test the hypothesis is the t-test for one mean and it will be a left-tailed test. Data Analysis Preparations

Hypothesis Testing for Regional Real Estate Company 3 Sample Size Mean Median Standard Deviation 750 $265.73 $204 $160.26 The samples in the histogram show that the data is skewed to the right, with a center median of $204 per square foot, while the data spans a wide range of variance from $104 to $996. The conditions are assumed to be met to conduct a t-test because all data was randomly collected through means of simple random sampling, no observations affect any other observations, and the sample size is large enough with no outliers present. The test significance level for this test is a=0.05. Calculations Sample Mean Standard Error $265.73 5.85

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Hypothesis Testing for Regional Real Estate Company 4 The appropriate test statistic for this test is the t-statistic. Using the equation, (mean- target)/standard error, ($265.73-$280)/5.8518= -2.4393. Since the salesperson is assuming the square foot price is lower than $280 in the Pacific region, a left-tailed test will be used. Using =T.DIST(-2.4393,749,1) = 0.0075. Excel Function Type of Test =T.DIST.RT([test statistic], [degree of freedom]) Right-tailed =T.DIST([test statistic], [degree of freedom], 1) Left-tailed =T.DIST.2T([test statistic], [degree of freedom]) Two-tailed Referencing to a normal curve graph, the p-value and test statistic would fall to the bottom left of the curve. Since the test statistic is negative, the value would fall 2.4393 standard deviations below the mean, assuming a mean of 0 and standard deviation of 1. Test Decision The relationship of the p-value to the significance level will determine if the null hypothesis is accepted or rejected if the p-value is less than the significant level of 0.05. The null hypothesis will be rejected because the p-value of 0.0075 is much less than 0.05. This p-value shows that the statement of cost of square footage in the Pacific region is equal to $280. Conclusion The null hypothesis of the cost per square footage of homes in the Pacific region being rejected relates to my testing because the calculated p-value of the square foot cost data is lower than the significant level of 0.05. The conclusion of the hypothesis is statistically significant

Hypothesis Testing for Regional Real Estate Company 5 because it proves that the advertisement would be false. There is enough data to support the alternative hypothesis and reject the null hypothesis.

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