excel assignment , statistics and probablity, report needs to be word file but i have attached excel file to get information
Statistical Modelling Assignment
BUS708 Statistics and Data Analysis Statistical Modeling Assignment [Pick the date] Student Id/Name
Section 1
Introduction
(a) The given task aims at analysing the trends with regards to methods of tax lodgement using the provided dataset 1. In addition, another dataset known as Dataset 2 has been collected based on information obtained from international students studying in our university. Based on the given sample, estimates need to be made about the proportion of taxpayer population which would lodge tax returns through tax agent. Also, the potential relationship between tax lodgement method choice with age and income has also been analysed through the use of appropriate statistical tools. Besides, the relationship between income and total deduction has also been explored based on the dataset 1 provided.
(b) The provided Dataset 1 constitutes of the variables mentioned below,
Dataset 1 has been obtained from data collected by the ATO and therefore this data would be referred to as secondary data. The quantitative variables are total income amount and total deduction amount which are captured using ratio measurement scale. The tax lodgement method is not a quantitative variable but a categorical one. Gender represents a dummy variable. Also, age is a variable of quantitative type owing to numerical values but the scale of measurement is ordinal. The first five cases are highlighted as shown below.
(c) The dataset 2 as mentioned above has been obtained through survey of international students at the campus and hence would be primary data. However, there is high probability of bias being present considering the usage of a non-probability sampling technique known as convenience sampling. Also, the given data collection is not random since data was collected based on assessibility and convenience. The data collected has been limited to three variables namely gender, age and the lodgement method.
Section 2
Tax Lodgement Methods (data set 1)
a. The two lodgement methods i.e. tax lodgement through registered tax agent or through themselves are represented by numerical summary and graphical display.
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Numerical summary: Pivot table is made in order to represent the number of taxpayers who will either use tax agent or self-preparer lodgement methods to file the tax returns.
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Graphical display: Column chart is used to represent the numerical summary.
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b. The calculation of the 95% confidence interval for the proportion of taxpayers (population) who will hire registered tax agent to file the tax returns.
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1.96 |
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Number of taxpayers (sample) |
1000 |
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Taxpayers that would file tax lodgement with the help of registered tax agent |
732 |
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Proportion p (tax lodgement by tax agent)
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= 732/1000 =0.732 |
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Standard error
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Lower limit of confidence interval
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Upper limit of confidence interval
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95% confidence interval |
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c. Comment on the findings: It can be said based on the above calculations that 73.2% of the sample taxpayers have hired registered tax agent for filing the tax returns while the remaining would lodge the tax returns on their own and hence, they will not hire any tax agent. Further, the 95% confidence interval tells us that there is 95% chance that the proportion of taxpayers who would lodge the tax returns with the help of registered tax agent would fall within [0.7045 0.7595].
Section 3
Tax Lodgement Methods for international students (data set 2)
a. The two lodgement methods i.e. tax lodgement through registered tax agent or through themselves are represented by numerical summary and graphical display.
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Numerical summary: Pivot table is made in order to represent the number of international students who will either use tax agent or self-preparer lodgement methods to file the tax return claim in future.
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Graphical display: Column chart is used to represent the numerical summary of the lodgement method.
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b. The calculation of the 95% confidence interval for the proportion of international students (proportion) who will hire registered tax agent to file the tax returns.
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1.96 |
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Number of international students (sample) |
15 |
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International students who would file tax lodgement with the help of registered tax agent in future |
11 |
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Proportion p (tax lodgement by tax agent)
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= 11/15 =0.7333 |
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Standard error
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Lower limit of confidence interval
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Upper limit of confidence interval
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95% confidence interval |
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c. Based on the above shown numerical summaries and graphical displays, it can be concluded that for both the data sets 1 and 2, the lodgement method by tax agent is the option that is more preferred. Further, nearly 73% of the taxpayers and international students would hire tax agent for tax lodgement. Moreover, the range of confidence intervals for population proportion of taxpayers seems to be coincident but more importantly, there is similarity in the point estimate. Also, even though the confidence interval length hugely differ for the two datasets but the same should not be a matter of concern as it is mainly attributed to the immense difference in sample size being considered which leads to difference in corresponding sample errors.
Section 4
Tax Lodgement Methods and Age Group
a. The two lodgement methods i.e. tax lodgement through registered tax agent or through themselves for various age groups are represented by numerical summary and graphical display. It is noteworthy that the age groups are being captured in the form of numerical codes ranging from 0 to 11 with lowest number being assigned to the highest age group and highest number being assigned to the lowest age group.
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Numerical summary: Pivot table is made in order to represent the number of taxpayers who will either use tax agent or self-preparer lodgement methods to file the tax return claim in future based on their age group.
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Graphical display: Column chart is used to represent the numerical summary of the lodgement method.
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b. In this part, hypothesis testing needs to be done in regards to check that the two variables i.e. tax lodgement method used by the taxpayers and their age are dependent or not. The given level of significance (alpha) is 5%.
Hypothesis Testing
· The requisite hypotheses are illustrated below:
The two variables tax lodgement method used by the taxpayers and their age are not correlated i.e. lodgement method and age are independent.
The two variables tax lodgement method used by the taxpayers and their age are correlated i.e. lodgement method and age are not independent or dependent on each other.
· Chi square distribution is considered the suitable approach to find which of the hypothesis would be rejected or accepted. In order to determine the expected frequency of the given observations and degree of freedom, value of chi-square statistics and the p value, the excel add-ins i.e. KADD has been used. The final output obtained from the excel is given below:
· Decision rule
The hypothesis decision is based on comparison on the p value and level of significance. The null hypothesis would not be rejected when the derived p value is more than the given level of significance. On the other hand, null hypothesis would be rejected and alternative hypothesis would be taken into account only when the derived p value is lower than level of significance.
· Final result
It is clear from the above computation that the p value is 0.0002 while the level of significance is 0.05. The p value is far lower than the level of significance. Hence, it would be fair to conclude that null hypothesis would be rejected and thus, the accepted hypothesis would be alternative hypothesis. Therefore, the two variables tax lodgement method used by the taxpayers and their age are correlated i.e. lodgement method and age are not independent.
c. Based on the above hypothesis test, a statistically significant relationship between the tax lodgement method and age has been indicated. Further, a general trend emerges where it is apparent that the taxpayers who are young in age tend to have a higher likelihood of not availing the services of the tax agent. As a result, as the age of the taxpayer progresses, there is a higher likelihood of tax returns being filed through a tax agent.
Section 5
Tax Lodgement Methods and Total Income Amount
a. The two lodgement methods i.e. tax lodgement through registered tax agent or through themselves and the total income amount of taxpayers are represented by numerical summary and graphical display.
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Numerical summary: Pivot table is made in order to represent the number of taxpayers who will either use tax agent or self-preparer lodgement methods to file the tax return claim in future based on their income range.
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Graphical display: Column chart is used to represent the numerical summary of the lodgement method.
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b. The column chart clearly shows a long rightward tail (positive side) that indicates the presence of positive skew. The asymmetric shape represents that the distribution of total income in lodgement method does not follow normal distribution. In this scenario, median would be considered as suitable option to comment on the central tendency of the data distribution since the mean might be influenced by presence of extreme values or outliers. Also, in case of lodging tax returns through tax agent, there is clear presence of outlier on the higher side as apparent from the above histogram.
Section 6
Total Income and Total Deduction Amount
a. In regards to determine the correlation between income and deduction amount for taxpayers, the numerical summary and graphical display of the data represented is highlighted below.
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Numerical summary: Summary statistics has been generated.
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Graphical display: Scatter plot is used to examine the exact correlation between income and deduction of the taxpayer.
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b. The scatter plot with regression line represents that the slope of line is positive and the correlation is positive. Further, the strength of the correlation can be found by taking the value of R square. Higher the value of R square, stronger would be the correlation between the variables. In this case, the value is very near to zero i.e. 0.0234 and thus, the conclusion can be made that total income and total deduction are weakly correlated. But the positive value of slope indicates that as the income of the taxpayers increases, then the deduction for tax purposes will also increase. For every one dollar increment in the total income of taxpayer, there would be an incremental deduction to the extent of $ 0.0068.
Section 7
Conclusion
The above analysis clearly reflects that the more prevalent method of lodging tax returns is through the registered tax agent. However, there are variations observed in this trend based on the underlying age and income of the taxpayer. It has been observed that the young taxpayers are more inclined to lodge the tax returns on their own without availing the services of tax agent. On the other hand, taxpayers with higher income also have higher tendency to file tax returns through tax agent. Also, the trend with regards to lodgement method is quite similar both amongst Australian taxpayers and also international students considering the similar findings. Besides, the correlation between income and deduction on income is positive but very weak and therefore not significant.
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