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Descriptive Statistics by Dwelling Type

Question:

Discuss about the Descriptive And Inferential Statistical Techniques.

A firm which is involved in housing construction wants to undertake a major housing development and needs to do analysis of the same for which information about the ongoing pricing and preferences of the customers need to be considered. A sample data has been performed in order to enable the analysis of the prices of houses and units that are located in Wollongong, Sydney and New Castle. Through the analysis, the company can obtain vital information in relation to the various combinations in terms of region, view and type which can fetch higher prices and essentially can also narrow down on the existing prices.

The given sample lists down the price of houses and units. It takes into consideration the region and also whether ocean view is available or not. For this data, descriptive statistics tools need to be applied so as to highlight the key characteristics of the provided sample data.  Further, based on the sample data inferences need to be derived based on the population data through the use of inferential statistics techniques such as hypothesis testing. Through this statistical analysis a comparison needs to be facilitated between various parameters which could highlight the prevailing price trends which could be then used by the company (Hair et. al., 2015).

The descriptive statistics aims to describe the characteristics of the sample data available through the use of various measures of central tendency and dispersion as they provide valuable information about the underlying shape and also helps in highlighting key trends which further can be validated for the population using the inferential statistical tools.

The descriptive statistics as per the dwelling type are as highlighted below.

From the above, it is apparent that the average price of houses seems to be higher in comparison to units. Also, there are certain houses which have quite high price leading to a rightward tail as is apparent from a positive skew. On the contrary, unit prices have a slight negative skew. Neither of the distributions would be normal owing to presence of skew. Dispersion seems to be low to moderate for both the type of dwellings even though it is slightly higher for houses in comparison to the units (Flick, 2015).

The descriptive statistics as per the underlying region where the underlying dwelling is located are as highlighted below.

Descriptive Statistics by Region

It seems evident from the above that there seems a significant difference in average prices in the various regions with Sydney having the maximum price and Newcastle having minimum prices. Further, for all the regions there is a positive skew presence which highlights non-normality and also presence of dwellings which have significantly high prices. The dispersion for the prices in various regions seems to be low when viewed in terms of mean which implies that for each region there seems to a different price band with limited overlapping (Hillier, 2006).

The descriptive statistics based on the presence or absence of the ocean view are as indicated below.

From the above, it is apparent that there does not seem any significant difference in the price of dwellings with or without an ocean view. A positive skew is observed for both which implies a tail on the right and hence the underlying distribution would not be normal. The dispersion as captured by standard deviation is quite comparable and remains moderate. However, the range for the dwellings with ocean view seems higher than the dwellings which lack ocean view. Thus, it might be possible that assuming everything else as the same, the ocean view might add a premium to the price (Hastie, Tibshirani and Friedman, 2011).

The inferential statistical techniques are deployed to derive information about the population based on the given sample information. Various claims are made which need to be checked based on the statistical data available from the sample through the application of hypothesis testing.  Using this technique, the various claims have been tested as highlighted below.

House Prices > Unit Prices

The requisite hypothesis to be tested is highlighted below.

Null Hypothesis (H0): µHouse = µunit

Alternative Hypothesis (H1): µHouse > µunit

For the comparison of the means of the above two independent samples, the requisite test would be T test since the standard deviation of the population is not known.

Considering the sample size is same for both the samples, equal variance option has been chosen in excel for the performance t test. The relevant output obtained from excel is as highlighted below.

Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis test is single tail and hence the applicable p value would be one tail. The one tail p value has been computed as 0. Assuming the level of significance as 5% or 0.05, it is evident that the relevant p value is lower than this value which implies that the available evidence is ample for rejecting the null hypothesis and thereby allows for acceptance of the alternative hypothesis. Hence, it may be claimed with 95% confidence that the average house prices are higher than the average unit prices (Flick, 2015).

Descriptive Statistics by Ocean View


Ocean view houses command premium

The requisite hypothesis to be tested is highlighted below.

Null Hypothesis (H0): µOceanView = µNoOceanView

Alternative Hypothesis (H1): µOceanView > µNoOceanView

For the comparison of the means of the above two independent samples, the requisite test would be T test since the standard deviation of the population is not known.

Considering the sample size is not the same for both the samples, unequal variance option has been chosen in excel for the performance t test. The relevant output obtained from excel is as highlighted below.

Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis test is single tail and hence the applicable p value would be one tail. The one tail p value has been computed as 0.043. Assuming the level of significance as 5% or 0.05, it is evident that the relevant p value is lower than this value which implies that the available evidence is ample for rejecting the null hypothesis and thereby allows for acceptance of the alternative hypothesis (Hair et. al., 2015). Hence, it may be claimed with 95% confidence that the average house prices with ocean view are higher than the average houses prices without the ocean view.

Difference in house prices in different regions

The requisite hypothesis to be tested is as highlighted below.

Null Hypothesis (H0): µSydney= µWollongong = µNewCastle

Alternative Hypothesis (H1): The average prices of houses in atleast one region are different from the others.

It is apparent that in the given case the average of more than two variables need to be compared and hence t test would not be feasible. Hence, the one column ANOVA is a suitable choice to compare the means (Hastie, Tibshirani and Friedman, 2011). The relevant output of this test obtained from Excel is as outlined below.

The requisite p value from the above output has come out as 0.00. Assuming the level of significance as 5% or 0.05, it is evident that the relevant p value is lower than this value which implies that the available evidence is ample for rejecting the null hypothesis and thereby allows for acceptance of the alternative hypothesis (Hillier, 2006). Hence, it may be claimed with 95% confidence that the average house prices in Sydney, Wollongong and New Castle are not the same and a statistically significant difference does exist.

Units situated in Wollongong with ocean view demand a price premium

Inferential Statistics Tests

The requisite hypothesis to be tested is highlighted below.

Null Hypothesis (H0): µOceanView = µNoOceanView

Alternative Hypothesis (H1): µOceanView > µNoOceanView

For the comparison of the means of the above two independent samples, the requisite test would be T test since the standard deviation of the population is not known.

Considering the sample size is not the same for both the samples, unequal variance option has been chosen in excel for the performance t test. The relevant output obtained from excel is as highlighted below.

Considering the alternative hypothesis has a > sign, it is apparent that the given hypothesis test is single tail and hence the applicable p value would be one tail. The one tail p value has been computed as 0.203. Assuming the level of significance as 5% or 0.05, it is evident that the relevant p value is higher than this value which implies that the available evidence is insufficient for rejecting the null hypothesis and thereby does not allow for acceptance of the alternative hypothesis (Hair et. al., 2015). Hence, it may be claimed with 95% confidence that the average unit prices in Wollongong with ocean view are similar to the average unit prices without the ocean view situated in Wollongong.

General Conclusion

Based on the results obtained from the statistical analysis carried above, it is apparent that the average price of houses is higher in comparison to the units. Also, evidence from sample data suggests that the houses having ocean view tend to command a price premium in comparison to those which lack the same. Besides, it is also evident that the average prices in the various regions (i.e. Sydney, Wollongong, Newcastle) are not comparable as they are significantly different from each other. Finally, it has also been seen that for units situated in Wollongong, the prices do not differ significantly with the presence or absence of an ocean view. However, one limitation of this is that the sample size is very small and hence it would be preferable if a larger sample size was available. The small sample size may be a problem especially for region based preferences in price since the filtered sample tends to become quite small and not very reliable.

Based on the above conclusion and the underlying objective of the study, it makes sense for the housing construction company to consider the above trends and implement the same in their choice of site and dwelling type constructed. It makes economic sense for the company to focus more on house construction rather than units since the former demands a price premium over the latter. Also, considering the high regional differences in price, if possible the company should look to undertake the project in Sydney as the price commanded by the project would be the highest amongst the locations considered.  Further, if possible, care needs to be taken to provide ocean view considering the underlying financials as the presence of ocean view could potentially bring in a price premium. However, it is essential that the cost considerations of the above suggestions should be considered by the builder and a suitable decision is undertaken by the construction company.

References

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.

Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning, 4th ed., New York: Springer Publications.

Hillier, F. (2006), Introduction to Operations Research, 6th ed., New York: McGraw Hill Publications

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[Accessed 03 March 2024].

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