MAT 240 Module Five Assignment
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Hypothesis Testing for Regional Real Estate Company
1
Hypothesis Testing for Regional Real Estate Company
Southern New Hampshire University
Hypothesis Testing for Regional Real Estate Company
2
Introduction
The Regional Estate Company has recently hired me to analyze the data that has been collected from recent home sales throughout the Pacific Region of the United States. The salesperson claims the average cost per square foot in this region is less than $280. He believes new advertisements will increase the average cost per square foot. It is my job to ensure this information is correct before he starts the project. To determine the answer, I generated a random
sample of 750 homes in the Pacific Region by using the =RAND() function in excel. I then selected the numbers and sorted them randomly from smallest to largest. From there, I used the first 750 for my data.
Hypothesis Test Setup
The population parameter is the mean of all the houses in all regions. The sample would be 750 houses from only the Pacific Region. The null hypotheses is µ=$280. The alternative hypothesis is µ>$280. My sample’s average is $265.
To find the answer the salesperson is looking for, I used a hypothesis test with a left-tail and a significance level of 0.05. Data Analysis Preparations
Hypothesis Testing for Regional Real Estate Company
3
Above is the histogram depicting the cost per square foot (x-axis) to the square footage in
the homes (y-axis).
Due to the sample being greater than 30, the distribution is roughly normal. The spread of
my sample of 750 homes is positively skewed and the significance value is 0.05. The assumptions do perform the identified test have been met. The center of data is between $104 and $230.
Calculations
To determine the calculations needed, I used excel formulas. For sample mean, I entered =AVERAGE() and selected the cost per square foot column and got $265. For the standard error,
I entered =STDEV.S(E:E)/SQRT(750) and it came out to be $5.93. The test statistic was found by entering: (sample mean-target)/standard error. That calculation came to -2.6104. Below you will see how the p-values were determined in excel for each type of test.
Excel Function
P Value
Type of Test
=T.DIST.RT([test statistic], [degree of freedom]) 0.9954
Right-tailed
=T.DIST([test statistic], [degree of freedom], 1) 0.0046
Left-tailed
=T.DIST.2T([test statistic], [degree of freedom]) 0.0092
Two-tailed
Test Decision
The p-value is less than the significance level of 0.05. With this information, we will reject the null hypothesis.
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Hypothesis Testing for Regional Real Estate Company
4
Conclusion
After calculating and analyzing data, there is enough evidence to support the claim that the square foot cost in the pacific is less than $280. The salesperson has a mean cost per square foot of $280. The pacific region cost per square foot is less than $280. This salesperson sells homes with a higher dollar per square foot amount. The salesperson is getting more money per square foot.
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