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Learning Team Reflection: Final Reflection
Learning Team Reflection: Final Reflection
QNT/351
University of Phoenix
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Learning Team Reflection: Final Reflection
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Hypothesis Testing Strategy
Throughout this course our team has performed different descriptive and inferential statistical
analyses in reference to the prices and sizes of homes. Raw data for these analyses has come
from the Real Estate dataset, which contains 105 entries. The paper for this week will performed
a one-sample test of hypothesis against a hypothesized value. The sample used in the analysis
corresponds to the prices of homes with sizes greater than 2200 sq. ft. Our hypothesis is that the
mean price of these homes is greater than $213,600. The test is done with the five-step
hypothesis testing methodology.
Research Question and Hypothesis
Do larger homes command higher prices? This is the research question our team will answer
through a hypothesis test. We will use a one-sample test of hypothesis to examine the research
question. Looking at the descriptive statistics results from prior weeks we know that the median
home price according to the Real Estate dataset is $213,600, and the median size is 2200 sq. ft.
Our hypothesis will be that the average price of homes larger than 2200 sq. ft. is greater than
$213,600. In other words, we are hypothesizing the mean price of homes larger than the median
home is greater than the median home price.
Verbally, the null and alternate hypotheses are:
Ho : the mean price of homes larger than 2200 sq. ft. is lower than or equal to $213,600.
H1 : the mean price of homes larger than 2200 sq. ft. is greater than $213,600.
Numerically, these hypotheses can be written as:
Ho : μ ≤ 213,600
H1 : μ > 213,600
Learning Team Reflection: Final Reflection
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Hypothesis Testing
The hypothesis test follows the 5-step methodology. The first step consists in stating the null and
alternate hypotheses. This was already done above.
The second step consists in selecting a level of significance. The test will be done with a
significance level of α = 0.05, which is a typical value used in business-related hypothesis
testing. The level of significance is important because it bounds the acceptable Type I error (the
error of having a false rejection) of the test. Here we are saying that the Type I error has at most
a 5% of happening.
The third step corresponds to identifying the appropriate test statistic. This is done based on the
size of the sample. Samples with size n≥30 use the z-test, while samples with size n<30 use the ttest. This is because when the sample size is at least 30 we can assume the sample standard
deviation closely approximates the population’s standard deviation according to the Central
Limit theorem. In our case there are 45 homes in the dataset with size greater than 2200 sq. ft.
Hence, n = 45 and we use a z-test statistic given by:
where
is the mean of the sample and σ its standard deviation.
Since the sample size is relatively large, we can be confident of having a small Type II
error (the error of having a false acceptance).
During step 4 the research formulates a decision rule taking the level of significance and
the test statistic into account. With an α=0.05 and a right-tailed z-test the critical value is z =
1.645. The decision rule is: reject Ho if z > 1.645. The decision rule is sketched in Figure 1.
Learning Team Reflection: Final Reflection
Figure 1. Sketch of the critical value and rejection region.
Finally, in step 5 the sample data is used to find the sample mean and standard deviation. The
test statistic is evaluated and compared against the decision rule and a decision is made. The
following is the output generated by MegaStat for this test:
Hypothesis Test: Mean vs. Hypothesized Value
213.6000
hypothesized value
235.8333
mean Data
49.9459
std. dev.
7.4455
std. error
45
n
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Learning Team Reflection: Final Reflection
2.99
z
.0014
p-value (one-tailed, upper)
221.2404
confidence interval 95.% lower
250.4262
confidence interval 95.% upper
14.5929
margin of error
As indicated by MegaStat, the test statistic is z = 2.99, which falls inside the rejection region
with a level of significance of 5%. As we can see, the p-value is a very small 0.0014. This
indicates that there is less than 0.15% probability of having a Type I error.
Why use a one-sample test method
In this research we used the one sample method to perform our test. A one-sample t-test helps
determine if the population mean is equal to the hypothesis test value. If the difference between
the sample mean and the test mean is larger than the sample mean, then it probably is not equal
to the test value or the test mean. This is an ideal situation to use a one sample test because we
have continuous data available from a single random sample. This test assumes that the
population is normally distributed. It is very important that data gathering is done properly and
the right audience is targeted. Bias data and influences can cause an impact to the final results
and so the end result might not be a true reflection on the findings.
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Learning Team Reflection: Final Reflection
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For example to test if smoking causes cancer, one has to make sure that research is performed on
people who smoke and got cancer and also people who don’t smoke and got cancer. Only
looking at one group will not provide a true and complete reflection of the situation.
Result and Decision
Complete the step five of the test and determine which of the following statements are true:

H0: the mean price of homes larger than 2200 sq. ft. is lower than or equal to $213,600.

H1: the mean price of homes larger than 2200 sq. ft. is greater than $213,600.
Based on the result we will determine if the business can categorize the data range in two
equal parts or not. Business will be able to determine if the policy: “of agent should focus on
showing houses up to 2300 square foot to the buyer with a budget of $213,600 or less” can be
implemented with less than 5% variance.
Conclusion
With our team performing different descriptive and inferential statistical analyses in reference to
the prices and sizes of homes, raw data for these analyses has come from the Real Estate dataset,
which contains 105 entries. We have explained why we chose to perform a one-sample test of
hypothesis against a hypothesized value and why the sample used in the analysis corresponds to
the prices of homes with sizes greater than 2200 sq. ft. Our hypothesis was that the mean price of
these homes is greater than $213,600. The test was done with the five-step hypothesis testing
methodology.
Learning Team Reflection: Final Reflection
References
Doane, D. P., & Seward, L. E. (2007). Applied Statistics in Business and Economics. Boston,
MA: McGraw-Hill/Irwin.
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