You have been accepted as an intern in a real estate company based in the heart of Sydney CBD. Your first job is to conduct an analysis of the current state of the Sydney rental market in various suburbs, particularly those with a significant number of international students like Sydney CBD, Ashfield, Strathfield, Parramatta, Epping, Eastwood, Hurstville, Bankstown, and so forth.

A. Individual task: locate and select data

For a suburb of your choice, each member of your group is required to collect data of ten 2-bedroom units / apartments for rent from a real estate website (realestate.com.au or domain.com.au). Each member must choose a different suburb. You are to record the following information about each of the 10 units for rent in each suburb:

a.Number of bedrooms

b.Number of bathrooms

c.Dishwasher (yes / no)

d.Walking distance to nearest train station (in minutes)

e.Minimum total travel time to Sydney Opera House by public transport (in minutes – according to weekday normal timetables)

f.Rent per week ($)

Q1. Determine and provide explanations for measurement levels of data specified above from (a) to (f).

Q2. List and present the data collected in a table (template as below – Table 1). For each observation, list the source where you have obtained the data.

## Individual Task: Question 1

The objective of the given report is to present an analysis of the real estate market in Sydney in the capacity of an intern working for a real estate company. For achieving the same, secondary data has been collected with regards to 40 properties equally divided amongst four suburbs and statistical analysis has been done so as to draw conclusions not only about the sample data but about the Sydney market in general.

**PART A – Individual Task**

**Question 1**

The measurement levels of the various variables are indicated below (Hastie, Tibshirani & Friedman, 2016).

- Number of bedrooms constitutes a numerical data with the measurement level being ratio. This is because an absolute zero can be defined in this case which is the value 0 and number of bedrooms cannot be negative.
- Number of bathrooms constitutes a numerical data with the measurement level being ratio. This is because an absolute zero can be defined in this case which is the value 0 and number of bathrooms cannot be negative.
- Presence of dishwasher would result in an answer yes or no. Hence, the given variable is categorical with measurement level as nominal as no automatic arrangement of responses in any logical order is possible.
- Walking distance (in minutes) would be in the form of numerical data with corresponding measurement scale as ratio. This is because an absolute zero can be defined in this case which is the value 0 and time cannot be negative.
- The minimum travel time to Sydney Opera House would be in the form of numerical data with corresponding measurement scale as ratio. This is because an absolute zero can be defined in this case which is the value 0 and time cannot be negative.
- Rent per week is a numerical variable with the minimum value as zero. As a result, the given variable would be categorised as ratio.

**Question 2**

Data has been provided in Excel. Need to be pasted from there.

**Question 3**

The five number summary for the weekly rent of various suburbs is indicated below.

Parramatta – It is apparent that 50% of the residential properties have a weekly rent less than equal to $ 530. There seems to be negative skew present in data as the lowest rent of $ 360 seems to be an abnormally low value which tends to deviate more than 2 times standard deviation from the median value.

Strathfield- It is apparent that 50% of the residential properties have a weekly rent less than equal to $ 542.5. There seems to be skew present in data as the lowest rent of $ 380 and highest value of $ 700 seems to be both abnormal which tend to deviate about 2 times standard deviation from the median value.

HurstVille - It is apparent that 50% of the residential properties have a weekly rent less than equal to $ 525. There seems to be negative skew present as 25% of the house rent per week tends to be lower than $ 437.5 while the lowest rent is $ 410. The rent distribution does not seem to be symmetric and hence does not adhere to normal distribution.

Bankstown- It is apparent that 50% of the residential properties have a weekly rent less than equal to $ 445. There seems to be positive skew present in data as the lowest rent of $ 560 seems to be an abnormally high value which tends to deviate more than 2 times standard deviation from the median value.

**Part B – Group Task**

**Question 4**

Based on the data obtained in question 3, it is apparent that the datasets for all the suburbs are skewed and hence the appropriate choice for the central tendency would be median and not mean. Comparing the median weekly rent across suburbs, it is apparent that there does not exist any significant difference in the median rents across Parramatta, Hurstville and Strathfield. However, the lowest median rent is found is Bankstown which is about $ 100 cheaper than the remaining suburbs. For the other suburbs besides, Bankstown, the standard deviation tends to be higher indicating high fluctuation in rent owing to the presence and absence of various desirable features. The fluctuations in rent are lower in Bankstown (Flick, 2015).

## Individual Task: Question 2

**Question 5**

Hypothesis testing would be deployed to test the claim. Let p_{1} indicate the proportion of units with weekly rent in excess of $ 500 which tend to have a dishwasher. Let p_{2} indicate the proportion of units with weekly rent less than or equal to $ 500 which tend to have a dishwasher.

The relevant hypotheses are as indicated below.

Null Hypothesis: p_{1}-p_{2}=0 which implies that there is no significant different in the proportion of dishwashers in the units with rent exceeding $ 500 a week and lower rent units.

Alternative Hypothesis: p_{1}-p_{2}>0 which implies that the proportion of dishwashers in the units with rent exceeding $ 500 a week is higher than the corresponding proportion for lower rent units.

For comparison of the two proportions, the relevant test statistic is Z. Also, the p value approach is used whereby the p value is compared with the assumed level of significance (0.05) to decide if the null hypothesis can be rejected or not (Hillier, 2016). The relevant output from Excel is indicated as follows.

Based on the above output, p value = 0.0008. Considering that p value is lesser than level of significance, hence the provided evidence is sufficient to reject the null hypothesis and accept the alternative hypothesis (Hair et. al., 2015). Hence, it can be concluded that the claim is true and hence the units with rent greater than $ 500 a week are more likely to have a dishwasher than the units which have lower rent.

**Question 6**

In order to explore the relationship between the walking distance to train stations and the weekly rent, the relevant diagram would be scatter plot which could represent both the nature of the relationship (linear or non-linear), direction (positive or negative) and strength (weak, moderate, strong) (Fehr & Grossman, 2013). The relevant scatter plot is indicated as follows.

From the above, it is apparent that there seems to be a weak positive relationship between the two variables. However, considering the deviation of the scatter points from the best fit line, it is apparent that the relationship does not seem significant which is confirmed by the low value of correlation coefficient and R^{2}. Thus, the notion that tenants tend to pay more for properties with easy access to train stations is not validated by the given data (Eriksson & Kovalainen, 2015).

**Question 7**

The average weekly rent in Sydney has been predicted based on the collected sample of observations in the manner highlighted as follows. It is imperative to note that T statistic has been used instead of Z because the population standard deviation of the residential properties weekly rents is not known.

## Individual Task: Question 3

Based on the above output, it may be concluded with 95% probability that the weekly rent for a unit/apartment in Sydney would lie between $ 482.37 and $ 535.13 (Flick, 2015).

**Question 8**

It is apparent that the 95% confidence interval for weekly rent in the two markets i.e. Sydney and Melbourne do not tend to overlap. This is indicative of a significant difference existing between the weekly rent in the two markets i.e. Melbourne and Sydney. Also, it can be concluded that the average weekly rent in Sydney is significantly higher than the corresponding value in Melbourne. IF the two intervals would have overlapped to some extent, then it would have been concluded that no significant difference would exist between the weekly rent of residential properties in Sydney and Melbourne. However, this is not the case here owing to the intervals for the two cities being non-overlapping (Harmon, 2015).

**Question 9**

Hypothesis testing would be deployed to test the claim. Relevant hypotheses are as indicated below.

Null Hypothesis: µ = $ 650 which implies that the minimum weekly rent in Sydney is $ 650

Alternative Hypothesis: µ < $ 650 which implies that the minimum weekly rent in Sydney is significantly lower than $ 650

The relevant test to be conducted in the given case is a one tail t test. The t test has been preferred ahead of z test owing to the standard deviation of weekly rent in Sydney being unknown (Flick, 2015). Further, the test is one tail owing to the alternative hypothesis. The relevant output of the test conducted in Excel is exhibited as follows.

Based on the above output, p value = 0.000. Considering that p value is lesser than level of significance, hence the provided evidence is sufficient to reject the null hypothesis and accept the alternative hypothesis (Hair et. al., 2015). Hence, it can be concluded that the claim that $ 650 is the minimum weekly rent in Sydney is incorrect.

**Conclusion**

On the basis of the above analysis, it can be concluded that the central tendency and deviation with regards to weekly rent is significantly lower for Bankstown while for the other three, these statistics are comparable. The sample data supports the conclusion that likelihood of the presence of dishwasher is higher in units with rent exceeding $ 500 a week. Also, there does not seem to be any significant relationship between distance from train stations and weekly rent. Further, it may be concluded with 95% probability that the weekly rent for a unit/apartment in Sydney would lie between $ 482.37 and $ 535.13. Besides, the above rent is significant higher than the corresponding estimate for Melbourne. Also, it is incorrect to claim that the minimum rent of a 2 bedroom apartment is not lower than $ 650.

**References**

Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research (3^{rd} ed.). London: Sage Publications.

Fehr, F. H., & Grossman, G. (2013). An introduction to sets, probability and hypothesis testing (3^{rd} ed.). Ohio: Heath.

Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research project (4^{th} ed.). New York: Sage Publications.

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of business research methods (2^{nd} ed.). New York: Routledge.

Harmon, M. (2015). Hypothesis Testing in Excel - The Excel Statistical Master (7^{th} ed.). Florida: Mark Harmon.

Hastie, T., Tibshirani, R. & Friedman, J. (2016). The Elements of Statistical Learning (4^{th} ed.). New York: Springer Publications.

Hillier, F. (2016). Introduction to Operations Research. (6^{th} ed.). New York: McGraw Hill Publications.

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