### Assignment | Statistics and Data Analysis

Added on - 28 May 2020

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Running head: STATISTICS AND DATA ANALYSISStatistics and Data AnalysisName of the Student:Name of the University:Author’s note:

1STATISTICS AND DATA ANALYSISTable of ContentsBackground:.................................................................................................................................................................................................2Description of Data:.....................................................................................................................................................................................2Used Software:.............................................................................................................................................................................................2Analysis of Data:.........................................................................................................................................................................................3Analysis of Single Variables...................................................................................................................................................................3Gender:................................................................................................................................................................................................3Age range:............................................................................................................................................................................................3Lodgement Process:.............................................................................................................................................................................5Total Monthly Amount of Income:......................................................................................................................................................6Total Monthly Amount of Deduction:.................................................................................................................................................8Lodgement Process and Gender:.........................................................................................................................................................9Analysis of Two Variables:.....................................................................................................................................................................9Lodgement Process and Range of Age:.............................................................................................................................................10Lodgement Process and total monthly amount of income:...............................................................................................................12Lodgement Process and monthly total amount of deduction:...........................................................................................................14Total Monthly Amount of Income vs. Total Monthly Amount of Deduction:..................................................................................15Testing of Hypothesis:...........................................................................................................................................................................16Lodgement Processes:.......................................................................................................................................................................16Total monthly Income Amount:........................................................................................................................................................17Total monthly Deduction Amount:....................................................................................................................................................17Tests of analysis of variance (ANOVA):...........................................................................................................................................18Student’s Paired two samples t-test:..................................................................................................................................................19Conclusion:................................................................................................................................................................................................19References:................................................................................................................................................................................................20

2STATISTICS AND DATA ANALYSISBackground:After the finishing of financial year, Australians lodge their income tax. Mainly in two ways that are by self-preparer and registered tax-paying agents, Australians lodge their income tax return. We are discussing and analysing briefly in this research report various inherent facts oflodgement processes lodges to the Australian Taxation Office (ATO).The report analyses the dataset. The dataset includes of few numerical and categorical variables like Gender, range of age, Lodgementprocess, Total income amount and Total deduction amount.The proportion of Australians who like to lodge a tax return with the help of a taxagent is a matter of interest. The variability among the age groups with respect to the lodging group is also observed. An essential relationbetween “total income” and “lodgement method” is being investigated. Finally, it is a matter of fact whether there is a relevance between totalincome and deduction amount or not.Description of Data:Internet resources helped to gather the data set. Hence, the dataset is secondary in nature. A total of 1000 samples are present in thedataset. Gender and Lodgement process are ordinal variables, range of age, total amount of income and total amount of deduction are thequantitative variables.Used Software:“Statkey” online software is used to accomplish the analysis. For analysis part of all the five variables, “One quantitative variable”, “Onecategorical variable”, “”One quantitative variable and one categorical variable”, “Two Categorical Variables” and “Two Quantitative Variables”are selected. Then, some randomised testing of hypothesis that are “Test for Single Mean”, “Test for Single Proportion”, “Test for Difference inMeans” as well as “Test for Difference in Proportions” are carried out. Lastly, some sophisticated randomized tests “ANOVA for Difference inMeans” and “ANOVA for Regression” are executed for reflection part.More to say that we have used “MSExcel” for accomplishing the analysis. Primarily, “Analysis ToolPack” named as “Data Analysis” inMSExcel is installed for advanced analysis. With the help of it, bar charts, box plots, linear regression analysis and hypothesis testing areincorporated with the installed “Data analysis tool”.

3STATISTICS AND DATA ANALYSISAnalysis of Data:Analysis of Single VariablesGender:The graph provides the frequency distribution of two types of genders. Note that, “1” indicates “Female” and “2” indicates “Male”. Theheights of bars are proportional to the frequencies of both the genders.Out of 1000 data, the number of “Female” (1) is 474 having proportion 0.474, whereas the number of “Male” (0) is 0.526 having theproportion 0.526.The pie chart shows the distribution of frequencies of both types of GendersRange of Age:

4STATISTICS AND DATA ANALYSISThe graph of spread of age of 1000 observations shows that the spread of age of the peoples varies from 0 to 11. The spread of ages ofgroup “9” has highest count (> 120) whereas the spread of ages of group “11” has lowest count (< 40).The histogram of range of ages shows the distribution of ages of all the 1000 samples. Most of the samples have range of age from 10 to11. Least occurrence of the range of ages is in the interval of spread of age from 1 to 2.The box plot provides the “Five number summary” of range of ages. It refers the distribution and location measures of all the samples.

5STATISTICS AND DATA ANALYSISThe descriptive statistics table of range of age of 1000 samples specify that age-group “9” has most count (125) and age-group “11” hasleast count (38). The average of spread of age is 5.859 and standard deviation is 3.127 (Holcomb 2016). Thehighest and least ranges of age are0 and 11. The 1stquartile, 2ndquartile (median) and 3rdquartiles of the distribution of spread of age are 3.5, 6 and 9 respectively.Lodgement Process:The graph of Lodgement process refers two different kinds of tax-lodging processes that are “self-prepare” and by “agents”. The numberof peoples whose tax-lodging method is by agent is significantly more than self-prepare.Out of all sampled data, 246 data (proportion = 0.246) lodges their tax by self-prepare and 754 data (proportion = 0.754) lodges their taxby agents.

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