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BUS708 Statistics And Data Analysis For Proportions Of Agent Lodgement

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  • Course Code: BUS708
  • University: Kings Own Institute
  • Country: Australia

Questions:

Section 1: Introduction

a. Give a brief introduction about the assignment, and include a short summary of a related article with a proper citation.
 
b. Dataset 1: Give a short description about this dataset. Is this primary or secondary data? What types of variable(s) is involved? Display the first 5 cases of your dataset.
 
c. Dataset 2: Explain how you collect the data and discuss whether your sample is biased. Is this primary or secondary data? What type of variable(s) is/are involved? You don’t need to display your data in this section.
 
2. Section 2: Lodgement Method – Dataset 1
Use Dataset 1
 
a. Using suitable graphical displays, describe the variable lodgement method for Dataset
b. Calculate a 95% confidence interval of the proportion of tax payers who lodge the tax return by using an Agent.
c. Give a short comment about your finding.
 
3. Section 3: Lodgement Method – Dataset 2
Use Dataset 2
 
a. Using suitable graphical displays, describe the variable lodgement method for Dataset
b. Calculate a 95% confidence interval of the proportion of tax payers who lodge the tax return by using an Agent.
c. Compare this result with the result in Section 2 and make a comment whether there is a difference between dataset 1 and dataset 2 in terms of lodgement method.
 
4. Section 4: Lodgement Method and Age Group
 
Use Dataset 1
a. Describe the relationship between the age group and lodgement method using suitable graphical display and numerical summary.
b. Perform a suitable hypothesis test at a 5% level of significance to test whether the two variables are associated.
c. Give a short comment about your finding.
 
Section 5: Lodgement Method and Total Income Amount
 
Use Dataset 1
a. Describe the relationship between total income and lodgement method using suitable graphical display and numerical summary.
b. Provide a comment about your result in part a (include a comment about the shape of the distribution, centre, spread and outliers).
 
6. Section 6: Total Income Amount and Deduction Amount
 
a. Describe the relationship between total income and total deduction using suitable graphical display and numerical summary, for each type of lodgement method.
b. Provide a comment about your result in part a.
 
7. Section 7: Conclusion
 
a. What can you conclude from your findings in the previous sections?
b. Give a suggestion for further research

 

Answer:

Introduction

a)Income tax filling in a part of the most important year ending task for any individual who comes under this tax filling line. Tax filing is a process that is being controlled by the income tax department which is a government controlled firm. They keeps a track of income of an individual that is being earned within a span of 1 year. Generally, an individual pays lots of taxes in throughout a year. Taxes are deducted during salary allocation, EMI taxes and all. They are being clearly depicted in the income tax file or the file carries a list of the different taxes as paid by an individual. Non-filling can lead to punishments of various sorts like capital punishment and jails punishments. Filling can draw lots of advantages like the taxes can get refunded as well with the some proper calculation in the return files. These calculations should be presented accurately with proper proofs for any kind of bills.  There is various way of filing taxes. E-filing, manual filing and all other ways can be used and this can be done by oneself or through a tax agent. A relevant journal can be sited here published by the PWC Corporation. The journal clearly states that there is a new inclusion in the tax filing system in Australia. People now have to issue General Purpose Financial Statements. This inclusion will affect certain sections and the effect will be in a large quantity. This kind of filing of the income tax returns needs a professional expert which will make it easy for filing the same. People who are quite known about the said sector have to learn a bit regarding the new thing. It’s better to appoint a tax agent for the purpose (Pwc.com.au 2018).

Tax agents are a very important medium for the completion of this procedure. They are specialized people dedicated for this process and have a perfect degree for the completion of the same. They are professionals who are generally employed by people and more than a single one for filing of this income tax. They are also government registered people. The filing process involves lots of calculations and construction of proper table which needs professionals. They can be done by individuals also who are quite aware of the process of filing and table construction but with an experiences agent, this filing can be done more accurately and it saves a lot of time. Specialized tax agents are quite easily available in the market for any kind of assistance. They are professionally trained people appointed for this purpose and they can be appointed by lot many of people at a time.  The topic of this task is to gain an idea regarding the use of these tax agents and whether they are being used by people for the tax filing. This is a secured procedure and it has been noticed with every passing time that the use of this agents for the taxation purpose has increased a lot.  This task uses a data regarding the usage of the tax agents and income of a person and the age gaps.

b)The first dataset consists of the answers of the questions like what is the gender, Age ranges, Income tax lodgment methods, total income amounts, total deducted amounts.  It depicts gender difference among people those lodges income tax through different procedures like by using agents and without using agents.  The total income of the people is also recorded and to be tested whether there is a relation between the tax filling process and the total income and also the deducted income for testing whether there is any relation between this variable and the tax filling procedures.

a)The second data set consists for the answers of the questions like the name of the country surveyed and the tax lodging methods, they will be tested with the point that what is exactly in the proportion of people using the tax agents for their filling and the country which is more involved in the process. Different countries can have a different alienation for this tax filling procedure and this will be tested through the second data set. 

 

Lodgment Method – Dataset 1

a) There are two lodgment methods as being described in the dataset. They are lodging of the tax through an agent and them lodging of the tax without using an agent (Christian 1994). The filing of taxes through this agent method is lot more easy since one does not need to get involved herself or himself for this. Anyone can appoint the agents and make a use of them for the said purpose with may be a little more payment but that is worth it (Hall and Wellner 2017). The lodgment methods and proportion of people using the two methods are depicted in the pie chart below:

b)There are lots of people who uses agents for the purpose of this income tax lodgment (Dance and Young 2014). A proportion can be calculated with the said category to have an idea of the proportion of people using agents for the lodgment (Lai, Rao and Vempals 2016).

No of taxpayers using agents:-

740

Total number of tax payers:-

1000

Confidence level

95%

Sample Proportion

0.74

Z Value

1.959964

Standard Error of the Proportion

0.013871

Margin of Error

0.027186

Cnfidence Interval:

 

Upper limit:-

0.767186

Lower limit:-

-1.21996

The proportion of people using agents is 0.74.  The upper 95% confidence interval for this proportion is 0.7671 and the lower 95% confidence interval is -1.21 (Rao 2015).

c) It can be commented from the calculations that most of the taxpaying people in Australia uses agents for their income tax filling (Li et al., 2016). There is lots of filling way and all of them can be smoothly handled through the agents (Kwon and Reis 2015). 

 

Lodgment Method – Dataset 2

(a)There are two different Income Tax lodgment methods that are by using agents and by directly filling without any agent (Chen, Buši? and Meyn 2015). There are always professional people available for the purpose. The data are given for four different countries and awareness for the use of these agents can be tabulated and depicted (Beran and Liu  2014). A graphical display can be made showing the number of people using different modes. The graph is attached below: 

It can be seen from he graph that 74% of the people use tax agents and 26% of the people doesn’t uses tax agents

b) A proportion of people can be calculated to see what exactly the proportion of using agent is and this can be used for decision making purpose for the future (Shuxia et al.,2014). Charts and calculation are being done and constructed and the resultant calculation are being done.

No of taxpayers using agents:-

152

Total number of tax payers:-

205

Confidence level

95%

Sample Proportion

0.741463

Z Value

1.959964

Standard Error of the Proportion

0.030579

Margin of Error

0.059935

Cnfidence Interval:

 

Upper limit:-

0.801398

Lower limit:-

0.681529

 

 

 

 

 

 

 

 

Figure 3:  proportion of people using agents for the tax lodgment outside Australia.

Source: (Created by author)

Confidence intervals can also be constructed to see what will be the level of variation. The calculated proportion here is 0.74 and the 95% higher confidence limit is 0.801 and the 95% lower confidence limit is 0.681. 

 


c)It can be tested whether the proportion of people paying their taxes through agents is equal in Australia and in other countries (Zheng et al., 2014). This test can be done through the hypothesis testing method. Hypothesis can be constructed as:

H0: The proportions are equal.

Vs.

H1: The proportions are not equal.

The calculations are done in the table below.

Level of significance

 

 

α

0.05

Critical Region

Critical Value

-1.9600

 

 

Sample Data

Sample 1 Data

Sample Size

1000

Count of 'Successes'

754

Sample proportion, p1

75.40%

Sample 2 Data

Sample Size

60

Count of 'Successes'

33

Sample proportion, p2

55.00%

 

Pooled estimate of proportion

74.25%

Standard Error

5.81%

z Sample Statistic

3.5099

p-value

0.0004

 

Decision

Reject Null Hypothesis

 

It can be seen from the table that p-value is less than levelof significance. Hence we reject the null hypothesis and conclude that The proportion of people using agent for tax lodgment is not equal in Australia and in other countries.

Section 4: Lodgment Method And Age Group:-

a) There can be a connection between opting different tax lodgment process and the age groups and this can be checked from the dataset. The data is plotted in a bar chart and that can be sited for any comparison (Arias-Castro, Mason and Pelletier 2016). The bar chart is attached below:-

 

It can be seen from the char that people using agent for tax lodgment has higher income levels than the people not using agents for tax lodgment. 

b)A hypothesis testing can be done for testing the relation between the age groups and the tax lodging procedures (Fan, Li and Wang 2017).  The testing hypothesis can be stated as:

H0: There is no connection between the age groups and the tax lodging procedures. 

Vs

H1: Age groups and tax lodging procedures are connected.

Statistics

 

a

0.95

df

11

χ2

46.26838104

p-value

2.89868E-06

χ2 Crit

4.574813108

sig

                     yes

 

Chi square test is being used for this test and the results can be interpreted as: tabulated (chi) is less than the calculated (chi) value and hence it can be concluded that the null hypothesis is false and the age groups and tax lodging procedures are connected.

c)It can be concluded from the test that the age groups and the tax lodging procedures are connected. It can happen that the modern generation is more alienated toward using agents and the older generations are not. They agents are the most shortcut methods and they can be used with ease.

Lodgment Method And Total Income Amount:-

a) Lodgment methods and the total income amount can be compared through the dataset. Among the two lodgment methods, income of people using agents for lodgment are recorded and income of people not using agent for lodgment are recorded. The table below shows the calculation: 

Lodgment

Average

St dev

Agent

38339.88

70226.3

not agent

26961.87

42013.48

 

 

 

Figure 7:  Analysis of lodgment amount and total income amount.

Source: (Created by author)

 

 

 

 

 

 

 

 

It can be seen that people using agents for their tax lodgment have more average income than the people not using agents for their tax lodgment.

agents. Summary of the report can also be presented.

using agents

 

not using agents

 

 

 

 

 

Mean

60601.24865

Mean

43878.84615

Standard Error

2581.57023

Standard Error

2605.565487

Median

46077.5

Median

37318

Mode

0

Mode

0

Standard Deviation

70226.30271

Standard Deviation

42013.48107

Sample Variance

4931733592

Sample Variance

1765132592

Kurtosis

78.18205454

Kurtosis

20.15880253

Skewness

6.84325103

Skewness

3.507426722

Range

1060166

Range

352377

Minimum

-7752

Minimum

0

Maximum

1052414

Maximum

352377

Sum

44844924

Sum

11408500

Count

740

Count

260

It can be said from the table that people using agents for their tax lodgment earns more than people not using agents. The minimum and the maximum income of people using tax agents is -7752 and 1052414. Again the minimum and the maximum income of people not using tax agents are 0 and 352377. Half of the people using agents have income below 46077.5 and half have income above that. And half of the people not using tax agents have income below 37318 and half have income above that. The 95% confidence interval of people using agents is 60326.7%, 653325.5%. Again the 95% confidence interval for people not using tax agents is 43977%, 49906%. The dataset of people using tax agents has 48 outliers and 7 people who are not tax agents have 7 outliers. That means48 people using agents have an income more than other and 7 people who are not using tax agents have income more than others. Again it can be said from the tablethat the income of both the category are skewed to the right. So it can be said that they has an average income less than the median. 

b)The distribution is skewed towards the right. So the average income is less than the median n both the cases. Distribution of people using agents for lodgment has 48 outliers trhat means 48 people have income more than normal and the people not using tax agents for lodgment have 7 outliers and that means 7 people have income more than normal. The center can be taken as mean in both the cases. The spread is the variation from the me3asn that is dispersion from mean and the spread is near about the same in both the cases. 

 

Total Income Amount And Deduction Amount:-

a)The relation between the total income and the total deduction amount can be tested. Total deduction amount is always expected to be dependent on the total income amount since deduction amount is the total quantity that is being deducted during the payments of the taxes and they can be related to the total income amount since higher income may ensure higher percentage of deduction. 

 

 

 

 

 

 

 

 

 

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

Multiple R

0.392401

 

 

 

 

 

 

 

R Square

0.153979

 

 

 

 

 

 

 

Adjusted R Square

0.153131

 

 

 

 

 

 

 

Standard Error

59352.39

 

 

 

 

 

 

 

Observations

1000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

1

6.4E+11

6.4E+11

181.6395

3.71E-38

 

 

 

Residual

998

3.52E+12

3.52E+09

 

 

 

 

 

Total

999

4.16E+12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

46259.63

2018.059

22.92283

9.26E-94

42299.5

50219.76

42299.5

50219.76

X Variable 1

4.03192

0.299162

13.47737

3.71E-38

3.444861

4.618979

3.444861

4.618979

 

 

 

 

 

 

 

 

 

Figure 11:  Analysis of deduction data and lodgment data.

Source: (Created by author) 

The numerical analysis of this part can be done through the regression testing procedure. There are two variables that are the deduction amount and the lodgment data. Anyone can be considered as a dependent variable and as an independent variable. The dependent variable are the one that is dependent on other variables like anything inside the dataset and they have to be calculated with the help of those variables (Korn et al., 2014). The independent variables are the ones that are not being touch with any other thing and they are measured indiviasually. The dependent variable is the y variables and the independent variable is the x variables. They can be tested through regression procedure in excel under the hypothesis:

H0: The lodgment amount and the deduction amount are not related.

Vs

H1:  The lodgment amount and the deduction amount are related.

Test suggests that the observed (f) is less than calculated (f). Observed F is the table value of the data that is being observed from the table and calculated F is the calculated value from the dataset. Hence, it can be said that the null hypothesis is not true and lodgment amount and deducted amount are related.

b)It can be commented here that there is a relation between the deducted amount and the lodgment amount and the relation is positive. That means if the lodgment amount increases then the deducted amount will also increase (Wang et al.,  2017). But they are not that strongly related. That means if does the deduction amount increases, then the lodgment amount will increase but not up to that extend.

Conclusion

a)It can be concluded from the analysis that people are now prone to use tax agents for income tax filing purpose and this point is valid for countries other than that of Australia. The proportions of people who are tax agent users are also quite high. There is a relationship between the age division and lodgment method. There is a positive relationship between total lodgment amount and the deduction amount.

b)A future research prospect regarding this matter can be: What is the people satisfaction level for using agents regarding income tax returns?. 

 

References:

Arias-Castro, E., Mason, D. and Pelletier, B., 2016. On the estimation of the gradient lines of a density and the consistency of the mean-shift algorithm. Journal of Machine Learning Research, 17(43), pp.1-28.

Beran, J. and Liu, H., 2014. On estimation of mean and covariance functions in repeated time series with long-memory errors. Lithuanian Mathematical Journal, 54(1), pp.8-34.

Chen, Y., Buši?, A. and Meyn, S., 2015, December. State estimation and mean field control with application to demand dispatch. In Decision and Control (CDC), 2015 IEEE 54th Annual Conference on (pp. 6548-6555). IEEE.

Chen, Y., Bušic, A. and Meyn, S., 2015. State estimation and Mean-Field Control with application to demand dispatch. arXiv preprint. arXiv, 1504.

Dance, D.R. and Young, K.C., 2014. Estimation of mean glandular dose for contrast enhanced digital mammography: factors for use with the UK, European and IAEA breast dosimetry protocols. Physics in medicine and biology, 59(9), p.2127.

Fan, J., Li, Q. and Wang, Y., 2017. Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(1), pp.247-265.

Hall, W.J. and Wellner, J.A., 2017. Estimation of mean residual life. arXiv preprint arXiv:1707.02484.

Jaime-Leal, J.E., Bonilla-Petriciolet, A., Bhargava, V. and Fateen, S.E.K., 2015. Nonlinear parameter estimation of e-NRTL model for quaternary ammonium ionic liquids using Cuckoo Search. Chemical Engineering Research and Design, 93, pp.464-472.

Korn, C.W., Sharot, T., Walter, H., Heekeren, H.R. and Dolan, R.J., 2014. Depression is related to an absence of optimistically biased belief updating about future life events. Psychological Medicine, 44(3), pp.579-592.

Kwon, D. and Reis, I.M., 2015. Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC). BMC medical research methodology, 15(1), p.61.

Lai, K.A., Rao, A.B. and Vempala, S., 2016, October. Agnostic estimation of mean and covariance. In Foundations of Computer Science (FOCS), 2016 IEEE 57th Annual Symposium on (pp. 665-674). IEEE.

Laver, R.D., Wiersema, U.F. and Bersten, A.D., 2014. Echocardiographic estimation of mean pulmonary artery pressure in critically ill patients. Critical ultrasound journal, 6(1), p.9.

Li, J., Chen, Y., Pan, S., Pan, Y., Fang, J. and Sowa, D.M., 2016. Estimation of mean and extreme waves in the East China Seas. Applied Ocean Research, 56, pp.35-47.

Pwc.com.au. 2018. Cite a Website - Cite This For Me. [online] Available at: https://www.pwc.com.au/tax/taxtalk/assets/alerts/ato-guidance-lodgment-28sep17.pdf [Accessed 20 Jan. 2018].

Rao, J.N., 2015. Small?Area Estimation. John Wiley & Sons, Ltd.

Shuxia, G., Yang, S., Ying, G. and Qianjin, H., 2014. Low complexity minimum mean square error channel estimation for adaptive coding and modulation systems. China Communications, 11(1), pp.126-137.

Wang, H.C., Minh, B.Q., Susko, E. and Roger, A.J., 2017. Modeling site heterogeneity with posterior mean site frequency profiles accelerates accurate phylogenomic estimation. Systematic biology.

Zheng, J., Zhang, Y.S., Shi, X.X. and Li, X.Z., 2014. Estimation of Mean Trace Length Based on Trace Maps Measured by GPS-RTK. In Applied Mechanics and Materials(Vol. 638, pp. 2141-2145). Trans Tech Publications.

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