MAT 240 Module Five Assignment
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Feb 20, 2024
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Hypothesis Testing for Regional Real Estate Company
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Hypothesis Testing for Regional Real Estate Company
Karen Morrow
Southern New Hampshire University
MAT 240: Applied Statistics
Instructor Jennifer Turner
November 27, 2022
Hypothesis Testing for Regional Real Estate Company
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Introduction
A Pacific region salesperson from the Regional Real Estate Company received an advertisement claiming that the average cost per square foot of home sales is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280. Knowing that the new advertisement would result in a higher average cost per square foot in the region, the salesperson would like to validate the statement before approving the use of the advertisement. To test this claim, a hypothesis test will be performed using a random sample of size 750 from the Pacific region data.
Introduction
The random sample of 750 was obtained by opening the spreadsheet for the Pacific region and using Excel’s rand function to assign random numbers to all the listed homes. These random numbers were presented in their own column titled random. The next step was utilizing Excel’s sort function by highlighting all the data in the spreadsheet, including the column titles, and sorting the information using the random column, which randomly sorted the data. The top 750 homes were then chosen to serve as the sample data.
Setup
The population parameter that is being tested is the mean cost per square foot in the Pacific region. In the hypothesis test, mu represents the population mean cost per square foot. The mean cost per square foot based on the new advertisement is $280 and the salesperson's claim is the mean cost per square foot in the Pacific region is less than $280. The null hypothesis is that the Pacific region’s cost per square foot is mu = $280.
The alternative hypothesis is the Pacific region’s cost per square foot is less than $280.
Hypothesis Testing for Regional Real Estate Company
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Because the salesperson believes that the mean cost per square foot is lower than the advertised cost per square foot, the alternative hypothesis test to be used is left-tailed with a significance level of 0.05.
Data Analysis Preparations
Using data for the Pacific region, a simple random sample of size 750 has been generated
for use in the hypothesis test. A random sample method is used so that each sample will have an equal probability of being chosen with a reduction in bias in the representation of the total population.
Descriptive Statistics of the Sample:
Sample Size
750
Mean
268
Median
206
Standard Deviation
162.592437
The histogram shows the distribution of the data is unimodal and skewed right (positively
skewed).
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Hypothesis Testing for Regional Real Estate Company
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The conditions to perform the identified test have been met in that the data has been collected randomly by means of simple random sampling and the data points are independent of one another. The t-distribution can be used as the sample size of 750 is sufficiently large and no outliers are present.
The appropriate test statistic would be the t-test where we solve for the test statistic using the equation t = (mean – target)/standard error. In this equation, the mean represents the mean of
the Pacific region which is 268. The target is 280 and the standard error is 5.94. The standard error was calculated by dividing the sample’s standard deviation by the square root of the sample (162.5924373 / √
750
). Therefore, the equation for t is (268-280) / 5.94 equals -2.06.
Sample Mean:
$268
(average of random sample)
Target:
280
Standard Error:
$5.94
sample_stdev / sqrt(n)
Test Statistic:
-$2.06
(sample_mean - target) / std error
Degrees of Freedom:
749
(sample number - 1)
Calculations
The left-tailed test where H0: u = 280 and H1: u < 280 was used to determine the p-value.
The p-value was calculated using the Excel function =T.DIST([test statistic], [degree of freedom]). In this case, the p-value is calculated with the function =T.DIST([-2.06],[749]). The p-value equals 0.01994787.
Test Decision
P-value equals 0.01994787 and the significance level is 0.05. Since the p-value is less than the significance level of 0.05, the null hypothesis is rejected. Sufficient evidence exists that the mean cost of square feet in the Pacific region is less than $280.
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Conclusion
The conclusion is the average cost of square feet in the Pacific region is less than $280. The test decision relates to the hypothesis in that the test determined the p-value (0.01994787) was less than the 5% significance level resulting in the rejection of the null hypothesis that the Pacific region’s mean average cost per square foot is $280. The hypothesis testing also revealed sufficient evidence to support the salesperson’s claim that the average cost per square foot in the Pacific region is less than $280.