MAT 240 5-3 Assignment: Means: Test of Hypothesis (1-Sample) Assignment PDF

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Summary

Design a hypothesis test and interpret the results using significance level α = .05 based on the 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 ...

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Hypothesis Testing for Regional Real Estate Company

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Hypothesis Testing for Regional Real Estate Company Darrellyn Mendez Southern New Hampshire University

Introduction The Regional Real Estate Company has hired me to analyze data. In this report, I will be analyzing real estate data for a salesperson from the company’s Pacific region. He has designed a

Hypothesis Testing for Regional Real Estate Company

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new advertisement that states, “the average cost per square foot of his home sales is above the average cost per square foot in the Pacific region.” He wants me to prove this statement is true before he approves the advertisement. I’ve been given a document with the house listing prices by region and will conduct my research from this. Setup The population parameter I am researching is the Pacific region’s mean cost per square foot (µ). Thus, the null hypothesis (H0) is µ = 275, and the alternate hypothesis (Ha) is µ < 275. I will be using a left-tailed test because I am trying to prove that the salesperson’s average cost per square foot is higher than the Pacific region’s average cost per square foot.

Data Analysis Preparations

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Curve 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -3 2.7 2.4 2.1 1.8 1.5 1.2 0.9 0.6 0.3 -

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8 1 4 7 3 6 9 2 5 0. 0. 0. 1. 1. 1. 2. 2. 2.

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The sample has a large spread meaning there is a lot of variability with the sample. It is rightskewed, non-symmetric, and unimodal. Conducting a left-tailed test will be the best option with this data because of the alternative hypothesis. Using the t-statistic test will be appropriate for testing this hypothesis. The significance level is 0.05.

Hypothesis Testing for Regional Real Estate Company Calculations Using the data analysis tool in excel, I calculated both the t-stat and the p-value of the data. Specifically, I determined these values using the t-test two-sample, assuming unequal variances option within the data analysis tool. In the table below are the calculations.

The colored lines in the graph above represent where the p-value and the t-stat would be. For example, the p-value (0.015) is green, and the t-stat (-2.148) is red.

Test Decision

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Hypothesis Testing for Regional Real Estate Company

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A p-value between 0 and 1 is how the level of statistical significance is expressed most often. Thus, the smaller the p-value, the more substantial the evidence to reject the null hypothesis. For example, the p-value from the sample is 0.015 and is less than the significance level of 0.05. From this, we would reject the null hypothesis since the mean cost per square foot is not greater than or equal to the salesperson’s mean cost per square foot.

Conclusion After thoroughly analyzing the data, I have concluded that the salesperson’s claim is valid. The alternative hypothesis is the salesperson’s claim that the average cost per square foot of his home sales is above the average cost per square foot in the Pacific region. And the null hypothesis is the Pacific region’s average cost per square foot is greater than or equal to the salesperson’s average cost per square foot. From the calculations, we can prove the salesperson’s claim that his average cost per square foot is above the Pacific region’s. Moreover, these calculations are statistically significant because the p-value (0.015) of the sample is below the significance level of 0.05....