Analysis of Sydney's Property Market: ECON1203 Milestone 2 Report

This report, prepared for ECON1203, analyzes the Sydney property market using inferential statistics. The study tests several claims about the market, including the mean total household income of purchasers, the mean internal size of apartments, the proportion of properties exceeding a certain price, the percentage of overseas purchases, and the proportion of non-owner occupied properties. The analysis involves hypothesis testing and the construction of confidence intervals to assess the validity of these claims based on a provided dataset. The report includes the statistical calculations, p-values, and conclusions regarding each claim, drawing on relevant statistical methods and referencing academic sources. The report also critiques a peer's work, evaluating its structure, presentation, and application of statistical concepts. The report concludes with a summary of the findings and their implications for understanding the Sydney property market.

Milestone 2: Sydney’s Property Market 1
ECON1203 Business and Economic Statistics
Milestone 2: Sydney’s Property Market
Name
Course Number
Date
Faculty Name

Milestone 2: Sydney’s Property Market 2
Milestone 2: Sydney’s Property Market
1. Mean total household income purchasers exceed $300,000
Null hypothesis: Mean = $300,000
Alternative hypothesis: Mean > $300,000
At 95% confidence interval, alpha = 0.05
The average and standard deviation of the household income for purchasers is shown below
Mean
360928.327
6
Standard Error
15982.0468
2
Standard Deviation
273568.575
3
Z score= 360928.328−300000
15982.047 =3.81
The p-value associated with this z-score equals 0.00007.
We conclude that we have enough evidence that the mean total average of household purchasers
is significantly greater than $300,000 (Aczel and Sounderpandian, 2008).
2. Mean interval size of apartment sold is 90sqm
The summary statistics of the interval size apartment are shown below
Mean
102.663822
5
Standard Error
2.05157761
1
Standard Deviation 35.1173520

Milestone 2: Sydney’s Property Market 3
2
The confidence interval of the square per metre is calculated as below
CI =mean± z∗standard deviation
√n
CI =102.66 ±1.96∗2.0515
The confidence interval is 98.64 to 106.68
Therefore, there is enough evidence that the mean interval size of the apartment is not 90sqm
because this value is not included in the 95% confidence interval
3. Majority of the properties exceed $1,500,000
The summary statistics are as shown below
Mean
2068973.09
6
Standard Error
81464.1332
7
Standard Deviation
1394441.34
6
The average price of the properties is $2,068,973.096
164 of the properties are above $1,500,000 which is approximately 56% (164/293) (Aczel and
Sounderpandian, 2008).
Less than 15% of the properties are sold overseas
Proportions of properties sold overseas equals to 0.215 with a standard deviation of
Null hypothesis: proportions of properties sold overseas = 0.15

Milestone 2: Sydney’s Property Market 4
Alternative hypothesis: proportions of properties sold overseas < 0.15
0ne-sample proportion test
p− phat
√ phat(1−phat )
n
= 0.215−0.15
√ 0.15∗0.85
293
= 0.065
0.0208 =3.125
The p-value associated with the z-score is approximately 0.009. We conclude that there is
enough evidence that the proportion of properties sold overseas are not less than 15% (Devore et
al., 2006).
4. More than 50% are no-owner occupied
Non-owner occupied properties are around 45.734%.
Null hypothesis: non-owner occupied = 50%
Alternative hypothesis: non-owner occupied > 50%
z score= p− phat
√ phat (1− phat)
n
0.457−0.5
√ 0.5∗0.5
293
=−0.043
0.0292 =−1.472
The z-score value equals to -1.472 and the p-value equals to 0.071
We conclude that we do not have enough confidence to conclude that more than 50% of the
properties are non-owner occupied (Cumming and Fidler, 2009).

Milestone 2: Sydney’s Property Market 5
References
Aczel, A. D. and Sounderpandian, J. (2008) Complete: Business Statistics, Association of
Business Information …. Available at: http://scholar.google.com/scholar?
hl=en&btnG=Search&q=intitle:McGraw-Hill/Irwin+=%3E?#1.
Cumming, G. and Fidler, F. (2009) ‘Confidence Intervals’, Zeitschrift für Psychologie / Journal
of Psychology, 217(1), pp. 15–26. doi: 10.1027/0044-3409.217.1.15.
Devore, J. et al. (2006) Statistics for Business and Economics, The American Statistician. doi:
10.1198/tas.2006.s59.