Bus708 Statistics And Data Analysis Assessment Answers

This assignment will test your skill to collect and analyse data to answer a specific business problem. It will also test your understanding and skill to use statistical methods to make inferences about business data and solve business problems, including constructing hypotheses, test them and interpret the findings.

 

Gender gap is the difference between the salary of men and the salary of women. The reasons of gender gap are not only because of discrimination in hiring, but also includes the different industries that women and men are working, as well as many other reasons. By using an edited subset of the sample file from the Australian Taxation Office (ATO), your task is to summarise and analyse several aspects of the salary and occupation of the different gender. In addition, you are also asked to suggest one relevant research question and then collect and analyse a dataset that will answer your research question.

Introduction:

1. The article is concern to do the analysis of salaries and occupation of different gender. The data is taken from Australian Taxation Office (ATO) for a particular location in Australia.

The necessity of the study is to distinguish about the relationship between salaries and occupation for different gender. This, the research question of the study can be considered as, whether there is a significance difference between the average salaries of male and female employees. To analyze the research question, the data collected for a particular location in Australia.

1. The dataset 1 is a taxation data provided by Australian Taxation Office (ATO) for a particular location in Australia. So, dataset 1 is a secondary data because it is obtained from another source. The dataset 1 have data for 1000 employees which consists information about Gender, Occupation code, salary/wage amount and the gift amount. The variable gender has divided into two categories as female and male, so it is a nominal level variable. The variable occupation code specifies the occupation of the employees which has divided into 10 categories, so it is a nominal level variable. The variable salary/wage amount indicates the salary of the employees, so it interval/ratio level variable. The gift amount indicates the gift or donation deductions, so it interval/ratio level variable.  

The first five values of the dataset 1 is,

Gender	Occ_code	Sw_amt	Gift_amt
Male	9	31304	0
Female	0	0	27
Female	2	86934	0
Female	4	28649	144
Female	3	69620	0

1. The dataset 2 collected by offline survey by asking questions to working employees about their gender, position and the salary/wage amount, so it is a primary data.

The dataset covers 50 values which are large enough to provide unbiased of the study.  The variable gender has been divided into two categories as female and male, so it is a nominal level of measurement. The variable occupation code indicates the occupation of the employees which has been divided into 10 categories, so it is a nominal level of measurement. The variable salary/wage amount indicates the salary of the employees, so it interval/ratio level of measurement.

Descriptive Statistics:

1. The graph for the relationship between variable Gender and the occupation is shown below:

Out of 1000, 21 male and 32 female employees were sales workers, 76 male and 18 female employees were technicians ate trades workers, 97 male and 96 female employees not listed their occupation otherwise it is not specified, 25 male and 95 female were clerical and administrative workers, 59 male and 29 female were laborers, 26 male and 57 female were community and personal service workers and 77 male and 87 female employees were professionals.

1. The graphical relationship between variable Gender and the salary/Wage amount is shown below:

The female earns about 39% of the total salary and male earns is about 61% of the total salary.

1. The numerical summary for the relationship between variable Gender and the salary/Wage amountis shown below:

Row Labels	Average of Sw_amt	Max of Sw_amt3	Count of Sw_amt2	StdDev of Sw_amt4	Sum of Sw_amt
Female	33841.72	308183	478	33428.35	16176341
Male	48181.46	308183	522	46863.41	25150721
Grand total	41327.062	308183	1000	41596.55031	41327062

The number of female employees is 478 and male employees is 522. The average salary of 478 female employees is about $33841.7 and the average salary of 522 male employees is $48181.46. The maximum salary of a female employee is $308183 and the maximum salary of a male employee is $308183. The total salary of female employees is $16176341 and the total salary of male employees is $25150721.

1. The graphical summary for the relationship between variable Salary/Wage amount and Gift amount is shown below:

For Consultants, apprentices and type not specified or not listed, the sum of gift amount is about $5582 and sum of salary and wage amount is about $3494488. For Professionals, the sum of gift amount is about $31058 and sum of salary and wage amount is about $10648470. For Machinery operators and drivers, the sum of gift amount is about $1523 and sum of salary and wage amount is about $2712048. For laborer, the sum of gift amount is about $11305 and sum of salary and wage amount is about $3146829.

Inferential Statistics:

16. The Professionals get 16.40% of the total salary in which female earns 8.70% and male earns 7.70%. The Clerical and Administrative Workersget 12% of the total salary in which female earns 9.50% and male earn 2.50%. The Technicians and Trades Workersget 9.40% of the total salary in which female earn 1.80% and male earn 7.60%. The top salary employees does not listed or not specified their Occupation, and the top salary is 19.30% of the total salary in which female earns 9.60% and male earn 9.70%. The results of overall salary percentage for gender corresponding to each occupation is shown below:

Occupation	Female	Male	Total
Occupation not listed/ Occupation not specified	9.60%	9.70%	19.30%
Managers	2.90%	5.10%	8.00%
Professionals	8.70%	7.70%	16.40%
Technicians and Trades Workers	1.80%	7.60%	9.40%
Community and Personal Service Workers	5.70%	2.60%	8.30%
Clerical and Administrative Workers	9.50%	2.50%	12.00%
Sales workers	3.20%	2.10%	5.30%
Machinery operators and drivers	0.20%	4.40%	4.60%
Laborer’s	2.90%	5.90%	8.80%
Consultants, apprentices and type not specified or not listed	3.30%	4.60%	7.90%
Grand Total	47.80%	52.20%	100.00%

1. The one sample Z-test will be used to test whether the proportion of machinery operators and drivers who are male is more than 80%, the hypothesis to test the claim can be defined as:

The null hypothesis is . And, the alternative hypothesis.

The proportion of male the Machinery operators and drivers is about 96%.  The calculations are done in excel, the calculated value of the Z-test statistic is 4.00 and the corresponding P-value for the upper tailed test is 0.000. The P-value of the test is less than 5% level of significance, so the null hypothesis of the test gets rejected.

Hence, the proportion of machinery operators and drivers who are male is more than 80%.

1. Two-sample t-test will be used to test whether there is a difference in salary amount between gender. The hypothesis can be defined as,

The null hypothesis is that the mean salary of male and female is equal.

And, the alternative hypothesis is the mean salary of male and female is different.

The ratio of the variance of male sample and female sample is greater than 1.5. So, the independent sample t-test will be useful. The calculations are done in excel, the value of the test statistic is 5.60 and the corresponding P-value of the two-tailed test is 0.000. The P-value of the test is less than 5% level of significance, so the null hypothesis of the test gets rejected.

Hence, salary of male and female differ significantly.

1. Two-sample t-test will be used to test whether there is a difference in salary amount between gender. The hypothesis can be defined as,

The null hypothesis is that the mean salary of male and female is equal.

And, the alternative hypothesis is the mean salary of male and female is different.

The ratio of the variance of male sample and female sample is greater than 1.5. So, the independent sample t-test will be useful. The calculations are done in excel, the value of the test statistic is 0.4391 and the corresponding P-value of the two-tailed test is 0.664. The P-value of the test is greater than 5% level of significance, so the null hypothesis of the test does not gets rejected.

Hence, salary of male and female not differ significantly.

Conclusion:

1. Out of 1000, 21 male and 32 female employees were sales workers, 76 male and 18 female employees were technicians ate trades workers, 97 male and 96 female employees not listed their occupation otherwise it is not specified, 25 male and 95 female were clerical and administrative workers, 59 male and 29 female were laborers, 26 male and 57 female were community and personal service workers and 77 male and 87 female employees were professionals.

The female earns about 39% of the total salary and male earns is about 61% of the total salary.

The number of female employees is 478 and male employees is 522. The average salary of 478 female employees is about $33841.7 and the average salary of 522 male employees is $48181.46. The maximum salary of a female employee is $308183 and the maximum salary of a male employee is $308183. The total salary of female employees is $16176341 and the total salary of male employees is $25150721.

For Consultants, apprentices and type not specified or not listed, the sum of gift amount is about $5582 and sum of salary and wage amount is about $3494488. For Professionals, the sum of gift amount is about $31058 and sum of salary and wage amount is about $10648470. For Machinery operators and drivers, the sum of gift amount is about $1523 and sum of salary and wage amount is about $2712048. For laborer, the sum of gift amount is about $11305 and sum of salary and wage amount is about $3146829.

The Professionals get 16.40% of the total salary in which female earns 8.70% and male earns 7.70%. The Clerical and Administrative Workers get 12% of the total salary in which female earns 9.50% and male earn 2.50%. The Technicians and Trades Workers get 9.40% of the total salary in which female earn 1.80% and male earn 7.60%. The top salary employees do not list or not specified their Occupation, and the top salary is 19.30% of the total salary in which female earns 9.60% and male earn 9.70%. The results are shown below:

The proportion of male the Machinery operators and drivers is about 96%, the proportion of machinery operators and drivers who are male is more than 80%.

The salary of male and female differ significantly in population and the salary of male and female not differ significantly in sample.

The result of population and sample is different, so the study is not providing accurate results. So, the data provided by the Australian taxation office may not be accurate and may be old. So, the researcher should do the analysis for the current data.