BUS708 Statistics And Data Analysis

Section 1

This assignment looks at primary and secondary data on properties, in terms of their weekly rent, dwelling type( flat/house), no of bedrooms, and bond amount paid . It covers 4 different suburbs.  It reports on a variety of questions relating to these parameters. ?

In dataset 1, we use primary data on the basis of interview of 5 students on their weekly rent. This sample can be biased as it uses respondents from my university campus only, so that its applicability across Australia is questionable. The sample size is also low as we use only 5 respondents. It will be inappropriate to use this small dataset to make any conclusions about the whole University.   ?

Dataset 2 is larger as it has 500 observations. It is secondary data on weekly rent paid, dwelling type (flat/house), no of bedrooms, and bond amount paid . It covers 4 different suburbs, and provides their post codes as well. The first 5 cases of your dataset are shown below.

Section 2

THE following table gives a numerical summary of the data. Median > mean which implies negative skewed distribution. The data is left skewed. ?The spread of data is high at a variance of 1032.5. As we can see students 5 has highest rent of $165, while student 2 has lowest rent of $90.

Section 3:

1. Using the data relating to Dwelling Type, we show that there is predominance of flats- 462/500 stay in flats. The majority students stay in Parramatta. (163/500). In Sydney no student from our sample set stays in houses.

The bar chart shows the same information in a graphical form. The predominance of flats (in blue) is clear, as is the preference for Parramatta and Sydney. ?

The proportion of House as a dwelling type is 38/500 = sample proportion= p

Ho: p= 0.1

H1: p < 0.1

Sample proportion = 38/500 = 0.076

Test value = (0.076 – 0.1)/ SE where SE = (0.076 *.924 /500)^.5 = 0.0118

Test value =  - 0.024/0.0118 = -2.015. Using a 5% level of significance, the critical z value is -1.645. as test value is > critical value in absolute terms we conclude that we do not accept the null hypothesis. There is evidence that proportion of Houses is less than 0.1.

Those who want to rent a house can use this data to see that less than 10% of existing students stay in houses. In Sydney no one stays in houses. This points to some advantages of flats, which are beyond discussion here. A simple look at this data tells us that students prefer flat by an overwhelming majority. It is advisable to stay in flats than houses as students.  ?

Section 4:

We now consider dwellings with 2 bedrooms only, and compare the weekly rent across different suburbs with average rent as the criteria. As we can see Auburn has the lowest average rent of $393.17, while Sydney has the highest average rent of $840.74.

We can examine if these differences are significant in a statistical sense using ANOVA test. In the results below we can see that the p value of the F test value is almost zero. This implies that the differences are statistically different.

 Since we are looking at 2 bedrooms rented places only, we can advise that in terms of rents Sydney is most expensive., while Auburn is less than half of Sydney rents. 

Section 5:

We use a scatterplot to examine the relationship between weekly Rent and Bond Amount below.

It is clear that there is strong linear association between them. We have some outliers ( around 3 data points as shown. The correlation coefficient is 0.953, which is very high. It shows a strong association, and also tells us 95.3% variation in rent is explained by variation in bond amount.

This suggests that a higher bond value is likely to result in higher rents. Students may choose lower bond values if they want to stay at cheaper places.

Section 6

A comparison of the weekly rent paid by international students and the weekly rent of properties on the market needs more data on students. This is because both datasets are samples. Their sizes are very different – 5 and 500. This is why any conclusions based on them will be incorrect and imprecise.

It is suggested that that the dataset for international students be expanded to include more data points as well as more information on bond amount, suburb, bedrooms, so that both sets are comparable.

References

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