Statistical Analysis of Weekly Rent in Sydney and Melbourne

This statistics assignment analyzes weekly rent data, focusing on central tendency measures like mean and median to compare rent prices across different suburbs (Auburn, Hurstville, and Parramatta). It investigates hypotheses related to rent proportions and the impact of dishwashers. The analysis ...Read More

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Question 4
Based on the relevant central tendency measures such as mean and median, it is apparent that
there exists significant difference in the weekly rent. The weekly rent in the Auburn suburb is
about $ 459 while the comparable amount for Hurstville is $ 625. Similarly, Paramatta has
also average weekly rent of 544. This represents significant difference in weekly rent based
on suburb. Also, the dispersion tends to vary amongst the different suburbs with the least
value observed in Hurstville where dispersion is comparatively less. This is the highest in
case of Auburn suburb (Flick, 2015).
Question 5
The relevant hypotheses are as highlighted below.
Null Hypothesis: p1 = p2
Alternative Hypothesis: p1> p2
P1 denotes the proportion of premium rent properties with dishwasher
P2 denotes the proportion of lower rent properties with dishwasher
In order to estimate whether the null hypothesis can be rejected or not, the p value approach
has been used. The relevant test statistics would be z. The test has been performed in excel
and the relevant screenshot is attached below.
From the above computation, p value = 0.5516

Assuming the level of significance as 5%, it is apparent that since p value is greater, hence
available evidence is insufficient to reject the null hypothesis and accept the alternative
hypothesis (Eriksson and Kovalainen, 2015). Hence, it may be concluded that the two
proportions do not differ and the claim of the industry report is incorrect.
Question 6
The relationship between the rent of two bedroom apartments and the easy access to public
transport can be highlighted using a scatter plot which is suitable considering that both the
variables have numerical values. The relevant scatter plot is indicated below.
It is apparent from the above scatter plot and the line of the best fit that the association
between the two variables is negligible. This is evident from the value of R2 which has come
out as 0.0017. This highlights that easy access to transport accounts for only 0.17% of the
variance of the weekly rent. Hence, it is clearly insignificant. The slope of the linear
regression line would be insignificant as the p value would be greater than 0.05 or the level of
significance (Hair et. al., 2015).
Question 7

The 95% confidence interval for average weekly rent in Sydney needs to be computed and
the following computation indicates the same.
From the above computation, it can be claimed with 95% confidence that the weekly rent in
Sydney would range between $ 488 and $ 552 (Flick, 2015).
Question 8
It is apparent that the two confidence intervals for weekly rent i.e. for Sydney and Melbourne
do not overlap. The weekly rent in Melbourne seems to be significantly different from that
witnessed in Sydney owing to non-overlapping of the two confidence intervals. It is clearly
apparent that average weekly rent in Sydney is significantly greater than the corresponding
levels witnessed in Melbourne where the average weekly rents are lower than $ 400 (Eriksson
and Kovalainen, 2015).
Question 9
The relevant hypothesis for the given hypothesis test are highlighted below.
Null Hypothesis: Minimum weekly rent in Sydney is $ 650
Alternative Hypothesis: Minimum weekly rent in Sydney is significantly different from $ 650
A two tail test would be performed using t as the test statistic since the population standard
deviation is unknown. The relevant computations have been performed in excel and the
corresponding screenshot is indicated below.

The p value has come out as 0.000. Assuming level of significance as 5%, it is apparent that
the available evidence is sufficient to reject the null hypothesis. Hence, the alternative
hypothesis would be accepted. This implies that the claim made by the study in regards to
minimum weekly rent being $ 650 is not supported by the current sample data (Hair et. al.,
2015).

References
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research (3rd ed.).
London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project (4th ed.). New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials
of business research methods (2nd ed.). New York: Routledge.