Hypothesis Testing & Rent Analysis

This assignment focuses on applying hypothesis testing to real estate data. Students analyze weekly rent samples from New Town and Hurstville, testing if the average rent in New Town exceeds $450 and comparing it to Hurstville's average rent. The assignment utilizes t-tests and provides calculated p-values to reach conclusions about significant differences in rental prices between the two suburbs.

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Hypothesis Testing & Estimation
STUDENT ID:
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Question 2
Sample and Population
The suburb 1 has been taken as New Town while the suburb 2 has been taken as Hurstville. A
sample data of 50 samples for the weekly rent has been collected for both the suburbs
(Source: https://www.realestate.com.au/buy ). The population of interest in each case would
be all the rented apartments which are located in the respective suburbs. From this
population, for the given task, 50 samples have been randomly selected.
Hypothesis Testing – Rent in New Town
The objective is to determine on the basis of the collected sample as to whether the average
weekly rent in New Town is greater than $ 450 or not. Since inference about the population
has to be drawn using sample, hence inferential statistics would be deployed.
The relevant hypotheses for the given test are indicated below.
Null Hypothesis (Ho): μ ≤ $450 i.e. the weekly rent of apartment in New Town is less than or
equal to $ 450
Alternate Hypothesis (H1): μ > $450 i.e. the weekly rent of apartment in New Town is more
than $ 450
It is apparent that the given hypothesis test would be a right tail test. Also, since the standard
deviation of the weekly rent of the population is not known, hence the appropriate test
statistic to be used would be t and not z.
Sample mean = $ 661.7
Sample standard deviation = $ 300.99
Sample size = 50
Hence, standard error = 300.99/√50 = 42.57
Thus, t statistics = (661.7-450)/42.57 = 4.97
Degrees of freedom = 50-1 = 49

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For the above degree of freedom and t stat = 4.97, the corresponding p value comes out as
0.00.
Assuming a 5% significance level, it would be fair to conclude that null hypothesis would be
rejected as the respective p value is lower than the assumed significance level. Hence, the
alternative hypothesis would be accepted which implies that the weekly rent of apartments
located in New Town is higher than $ 450.
Hypothesis Testing – Comparison of Rents
The objective is to determine on the basis of the collected sample as to whether the average
rent in suburb 1 (New Town) is greater than the average rent in suburb 2(Hurstville). Since
inference about the population has to be drawn using sample, hence inferential statistics
would be deployed.
The relevant hypotheses for the given test are indicated below.
Null Hypothesis (H0): μNew Town ≤ μHurstville
Alternative Hypothesis (H1): μNew Town > μHurstville
The appropriate test to be deployed t test for 2 independent samples as the underlying
standard deviation for the respective population is not known. The respective output obtained
from Excel is indicated below.
The relevant p value would be one tail which is 0.0499. Assuming a 5% significance level, it
would be fair to conclude that null hypothesis would be rejected as the respective p value is

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lower than the assumed significance level. Hence, the alternative hypothesis would be
accepted which implies that the weekly rent of apartments located in New Town is higher
than the weekly rent of apartments located in Hurstville.
Conclusion
Based on the collected sample weekly rents for apartment for the two suburbs, it would be
fair to conclude that the weekly rent for apartments located in New Town (Suburb 1) would
be greater than $ 450. Also, it may be concluded with 95% probability that weekly rents for
apartments in New Town are comparatively higher than the corresponding values in
Hurstville.