MAT 240 Module Five Assignment
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Southern New Hampshire University *
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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
Melanie Maxwell
MAT 240 Module 5 Assignment
Southern New Hampshire University
Hypothesis Testing for Regional Real Estate Company
2
Introduction
The purpose of this analysis is to assist the employees at the Regional Real Estate company determine if the information featured in their new advertisement is accurate. The salesperson is questioning the validity of the pricing for the cost per square foot, and would like further investigation analyzing the data. A random sample of 750 properties in the Pacific region was generated. A hypothesis test will be conducted and final conclusion will yield the results. Based on the results the advertisement cannot be approved if the null hypothesis is supported.
Hypothesis Test Setup
The information for the full population isn’t available. However, we do have a sample of 750. The population parameter being tested is the mean cost per square foot in the Pacific region.
In this test the average is being tested. The alternative hypothesis is that the mean cost per square
footage in the Pacific region would be less than $280. The null hypothesis is that the mean cost per square footage will be greater than $280. To determine which hypothesis is correct, I will use
a left-tailed t-test.
Data Analysis Preparations
To begin my analysis I generated the sample mean of the data set, which came out to be $263. The null hypothesis is $280 per square foot and the alternative hypothesis is less than $280
per square foot.
Hypothesis Testing for Regional Real Estate Company
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This histogram sample has generated a right skewed graph with a downward progression.
Most of the houses on this graph have a cost per square foot between 104 and 226. This sample is reflective of the Pacific region and not the entire national market. The test significance level is 0.05.
Calculations
Cost per Square Foot
Sample Mean
262.8756193
Target
280
Standard Error
5.806897003
Test Statistic
-2.948972688
Degree of Freedom
749
Mean
$262.88
Median
$201.59
Standard Deviation
159.0284239
We continued our analysis by calculating the test statistic. The test statistic was generated
using (mean-target)/standard error (263-280/5.80). I used the formula =T.DIST, calculated in excel as =T.DIST(-2.9489, 749, 1), this yielded a p-value of 0.001643787. This value is less than
the significance of 0.05.
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Hypothesis Testing for Regional Real Estate Company
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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
Test Decision
As previously stated the significance of 0.05 is less than our p-value so the hypothesis will be rejected. There is enough evidence that supports that the mean cost per square footage in the Pacific region is less than $280.
Conclusion
The salesperson has a mean cost of square foot of 280, and the Pacific region has a mean cost of square footage that is less than 280. The salesperson is getting more money per square foot for their clients than our region so we will be unable to use the advertisement.