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Hypothesis Testing for Regional Real Estate Company
1
Hypothesis Testing for Regional Real Estate Company
Leslie R. Rossner
Department of Mathematics, SNHU
MAT 240: Applied Statistics
Professor Jennifer Turner
February 11, 2024
Hypothesis Testing for Regional Real Estate Company
2
Introduction
This report analysis is to test the average cost per square foot in the Pacific Region to be less
than $280 to ensure the new advertisement for result in a higher average per square foot cost in
the region. By using the Excel RAND function, a truly random sample of 750 homes in the
Pacific Region can be created. This is done by copying and pasting all the numbers and using the
RAND function to select the random sample, and lastly sorting from smallest to largest and
selecting the first identified 750 that are listed. Hypothesis Test Setup
The mean cost per square foot in the Pacific region is the population parameter that is being
tested. The mean cost per square foot in the Pacific region is equal to $280, H0: µ= $280 and
is therefore defined as the null hypothesis. The mean cost per square foot in the Pacific region
is less than $280 is the alternative hypothesis in this Hypothesis Test Setup, which will be
using a left-tailed test.
Data Analysis Preparations
The cost per square foot target mean is $280, while the sample mean cost per square foot is
$264. The sample size is 750 homes. The cost per square foot sample median is $202 with a
standard deviation of 5.887. With the histogram right skewed, this indicates that the median
is less than mean, or in other words, the mean is greater than the median. The sample spread
is also the standard deviation while the mean is the center. In order to run the test, the
sample size needs to be at least 30 and random. Since the conditions to run the test are met
at 750 random samples, the test is able to be run with a significance level being 0.05 for this
sample.
Hypothesis Testing for Regional Real Estate Company
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Calculations
$264 is the sample mean of the cost per square foot with a standard deviation of 5.887. To obtain
the test statistic:
Sample mean – Target
Standard Deviation
which amounts to 264-280
5.887 = -2.742
The appropriate test statistic would be a left-tailed test and indicates the sample mean is less than
the target mean. This also identifies the relationship being a close distribution of the sample data
to the target data distribution. Using the left-tailed function in Excel, 0.003 is concluded to be the p
value for the sample.
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
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Hypothesis Testing for Regional Real Estate Company
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The blue area represents the 0.003 p value with -2.742 as the test statistic indicated by the thick black line.
Test Decision
To determine if a null hypothesis will be rejected or fail to be rejected, the significance level is
used. In this sample, the significance level is 0.05. The null hypothesis will be rejected if the p
value is less than 0.05, however, if the p value is greater than 0.05 then the null hypothesis will
fail to be rejected. Therefore, since the p
value for this sample is 0.003 and is less than 0.05, the
null hypothesis is rejected. Conclusion
The average cost per square foot in the Pacific region is concluded to be less an $280. The mean
cost per square foot for the null hypothesis is equal to $280 while the alternative null hypothesis
is less than $280. Since the p
value in this sample is less than 0.05, the null hypothesis will be
rejected. Since the p
value of this sample is less than the significance level, the conclusions are
statistically significant.