5-3 Assignment - Means, Test of Hypothesis
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Hypothesis Testing for Regional Real Estate Company
1
Hypothesis Testing for Regional Real Estate Company
Colleen Del Valle
Southern New Hampshire University
Hypothesis Testing for Regional Real Estate Company
2
Introduction
The purpose of this analysis is to analyze real estate data from the Pacific Region, to see if the average cost per square foot of a home is less than $280. I was able to generate a random sample by using the blank column ‘G’ and typing in the formula ‘=RAND()’ into ‘G2.’ The formula populated a random number, from there I copied the formula all the way down to the last
data set. Hypothesis Test Setup
The population parameter is the mean cost per square foot in the Pacific Region (
m
).
Null hypothesis, H
0
: µ = $280 per square foot.
Alternative hypothesis, H
1
<
$280 per square foot
For testing purposes, I will be using the left-tailed test as the left tailed test is used when the hypothesis asserts that the value of the parameter is less than the value asserted in the null hypothesis. Data Analysis Preparations
Descriptive Statistics
Sample Size
750
Sample Mean
$262
Sample Median
$203
Standard Deviation
162.490563
Hypothesis Testing for Regional Real Estate Company
3
The above model mirrors the cost per square foot for the Pacific Region with the x-axis being the cost per sq ft and the y-axis being the sample size. The shape of the histogram would be considered a multimodal because there are more then two “mounds.” With a skewness to the right because that is where the tail is. The center on the model is not in the center but to the left at $264 per sq ft and it is reflective of the spread or standard deviation being $162.50. The assumptions have been met being as the sample size is 750, and the sample mean is less than 280. The test significance level is α = .05.
Calculations
The sample mean for the cost per sq ft is $264, with the standard error being $5.93. To determine the test statistic, you must take the sample mean of 264 minus the target which is 280 then divide by 5.93. the equation will look like this, (264-280)/5.93 = -2.96910878. Now to calculate the p
value, you need to determine the best type of test to use, as I stated above, we will
be using a left-tailed test to complete the analysis. To calculate the p
value for a left-tailed test you need to figure out what your degree of freedom is, for this analysis the degree of freedom is taking the sample size of 750 and subtracting 1, that would make the degree of freedom 1. For
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Hypothesis Testing for Regional Real Estate Company
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the p value, input =T.DIST(test statistic, degree of freedom, 1). =T.DIST(-2.96910878, 749, 1) which equals 0.00154099 as the p
value.
In the curve graph above I have the test statistic or t-stat as I have labeled it and the
p
value. Test Decision
When comparing the p value to the significance level, the significance level is greater than the p
value. The p
value is 0.00154099 and the significance level is 0.05. With the p
value being less than the 0.05 we will reject the null hypothesis based off the supporting evidence above.
Conclusion
After viewing the data given to me by the sales representative stating that homes in the Pacific region cost less than $280 per sq ft, I am confident to agree with him as the data shows the cost per sq ft to be $264. The null hypothesis was rejected as it did not support what the sales representative claimed, and the alternate hypothesis was accepted as the cost per square foot is T-Stat
-2.96910878
P-Value
0.00154099
Hypothesis Testing for Regional Real Estate Company
5
lower than the average of $280. The mean cost per square foot in the Pacific region is $264 and the calculated p
value is 0.00154099. When the modifications are made to the advertisement it will be good to run.
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