Relationship Between Salaries, Occupation, And Gender

a.Give a brief introduction about the assignment, including your research question. 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 its limitation (e.g. 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.

a.Using suitable graphical display, describe the relationship between the variables Gender and Occ_code for Dataset 1. Make sure your graph shows the distribution of Gender for each Occ_code.

b.Using suitable graphical display, describe the relationship between the variables Gender and Sw_amt

c.Using suitable numerical summary, describe the relationship between the variables Gender and Sw_amt.

d.Using suitable graphical display, describe the relationship between the variables Sw_amt and Gift_amt.

a.List top 4 occupation based on median salary and find the proportion of the gender of those top 4 occupation.

b.Perform a suitable hypothesis test at a 5% level of significance to test whether the proportion of machinery operators and drivers who are male is more than 80%.

c.Perform a suitable hypothesis test at a 5% level of significance to test whether there is a difference in salary amount between gender.

d.Perform a suitable statistical analysis on dataset 2 (the one you collected) that will answer your research question.

Discussion & Conclusion

a.What can you conclude from your findings in the previous sections?

b.Give a suggestion for further research

a.The article is based on the study of relationship between the salaries of different gender in relation to the occupation of the taxation data of a particular location in Australia.

It is also need to the collection of data connecting the research question of business problem from a relative population and analysis of the collected data (dataset 2) using suitable statistical analysis. The business manager wants to know about the relationship between the salaries of different gender in relation to the occupation. So, the research question will be to know whether there is a significance difference between the average salary of male and female.

b.The dataset 1 holds the taxation data of a particular location in Australia which is provided by Australian Taxation office. So, the dataset is obtained for the other source which is Australian Taxation office, thus it is a secondary data. The dataset contains the data of 1000 employees which consists 4 variables as (Gender, Occupation code, salary/wage amount and the gift amount. The variable gender is divided into two categories as female and male, so the variables gender is measured into a nominal level of measurement. The variable occupation code indicates the occupation of the employees which is divided into 10 categories, so the variables occupation is measured into a nominal level of measurement. The variable salary/wage amount is the salary of the employees which contains numeric values, so it interval/ratio level of measurement and the gift amount indicates the gift or donation deductions which contains numeric values, so it an interval/ratio level of measurement.

The first five values of the dataset is shown below;

Gender	Occ_code	Sw_amt	Gift_amt
Female	2	32733	0
Female	5	13445	0
Female	1	50507	109
Male	0	0	0
Female	9	20489	0

c.The dataset 2 is collected by offline survey and asked to employees randomly about their gender, position and the income amount. So, the dataset is obtained by the survey, thus it is a primary data. The dataset contains 40 observations and collected randomly and also the sample size is greater than 30, so it can say that the collected data will be unbiased. The dataset contains the data of 40 employees which consists 3 variables as (Gender, Occupation code, salary/wage amount). The variable gender is divided into two categories as female and male, so the variables gender is measured into a nominal level of measurement. The variable occupation code indicates the occupation of the employees which is divided into 8 categories, so the variables occupation is measured into a nominal level of measurement. The variable salary/wage amount is the salary of the employees which contains numeric values, so it an interval/ratio level of measurement.

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

The above bar plot indicates that, most of employees not listed their occupation otherwise it is not specified. Out of 1000, 81 male and 77 female employees were professionals, 86 male and 16 female employees were technicians ate trades workers, 26 male and 92 female employees were clerical and administrative workers, and 21 male and 44 female employees were sales workers.

Dataset 2

b.The pie chart for the relationship between variable Gender and the salary/Wage amount is shown below:

The male earns 68% of the total salary and male earns 32% of the total salary.

c.The numerical summary for the relationship between variable Gender and the salary/Wage amount is shown below:

Gender	Average of Sw_amt	Count of Sw_amt	Max of Sw_amt	StdDev of Sw_amt	Sum of Sw_amt
Female	31768.51	461	308183	32603.49	14645283
Male	57830.74	539	839840	67008.17	31170769
Grand Total	45816.05	1000	839840	55466.19	45816052

The total number of female employees is 461 and the male employees is 539. The average salary of a female employee is $31768.51 and for the male employee is $57830.74. The maximum salary of a female employee is $308183 and the maximum salary of a male employee is $839840. The, total salary of a female employee is $14645283 and the total salary of a male employee is $31170769.

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

The salary wage for female employees is 31.97% and the gift wage for the female employees is 51.85%. The salary wage for male employees is 68.03% and the gift wage for the male employees is 48.15%

a.The top 4 occupation based on median salary and the proportion of the gender of those top 4 occupations is shown below:

Row Labels	Female	Male	Grand Total
Occupation not listed/ Occupation not specified	9.40%	11.80%	21.20%
Professionals	7.70%	8.10%	15.80%
Clerical and Administrative Workers	9.20%	2.60%	11.80%
Technicians and Trades Workers	1.60%	8.60%	10.20%

The top salary employees does not listed or not specified their Occupation, and the top salary is 21.20% of the total salary in which female earn 9.40% and male earn 11.80%. The Professionals get 15.80% of the total salary in which female earn 7.70% and male earn 8.10%. The Professionals get 15.80% of the total salary in which female earn 7.70% and male earn 8.10%. The Clerical and Administrative Workers get 11.80% of the total salary in which female earn 9.20% and male earn 2.60%. The Technicians and Trades Workers get 10.20% of the total salary in which female earn 1.60% and male earn 8.60%.

b.To test whether the proportion of machinery operators and drivers who are male is more than 80%, one sample Z-test will be used. The hypothesis of the test is given below:

The formula to calculate the value of the test statistic is given below:

The proportion of male the Machinery operators and drivers is about 93%. Now calculate the value of test statistic, the calculation are provided in Excel. The obtained results are shown below:

Z Test of Hypothesis for the Proportion
Null Hypothesis            p =	0.8
Level of Significance	0.05
Number of Items of Interest	93
Sample Size	100
Intermediate Calculations
Sample Proportion	0.93
Standard Error	0.0400
Z Test Statistic	3.2500
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0006
Reject the null hypothesis

c.According to the above results, the P-value of the test is less than 5% level of significance, so the null hypothesis of the test gets rejected. Thus, it can be concluded that the proportion of machinery operators and drivers who are male is more than 80%.

To test whether there is a difference in salary amount between gender, two-sample t-test will be used. The hypothesis of the test is given below:

The difference between the sample variances is, (4490095016.9213/1062987395.6461 =4.22) which is greater than 1.5. So, the separate variance t-test will be used for analysis.

Now calculate the value of test statistic, the calculation is provided in Excel. The obtained results are shown below:

Separate-Variances t-Test for the Difference Between Two Means
Hypothesized Difference	0
Level of Significance	0.05
Female Salary
Sample Size	461
Sample Mean	31768.50976
Sample Standard Deviation	32603.4875
Male Salary
Sample Size	539
Sample Mean	57830.74026
Sample Standard Deviation	67008.1713
Numerator of Degrees of Freedom	113129749452334.0000
Denominator of Degrees of Freedom	140546947310.5650
Total Degrees of Freedom	804.9250
Degrees of Freedom	804
Standard Error	3261.3260
Difference in Sample Means	-26062.2305
Separate-Variance t Test Statistic	-7.9913
Two-Tail Test
Lower Critical Value	-1.9629
Upper Critical Value	1.9629
p-Value	0.0000

According to the above results, the P-value of the test is less than 5% level of significance, so the null hypothesis of the test gets rejected. Thus, it can be concluded that there is a difference in salary amount between gender.

d.To test whether there is a significance difference between the average salary of male and female, two-sample t-test will be used. The hypothesis of the test is given below:

The difference between the sample variances is, (6068626974/2911806589 =2.08) which is greater than 1.5. So, the separate variance t-test will be used for analysis.

Now calculate the value of test statistic, the calculation is provided in Excel. The obtained results are shown below:

Separate-Variances t Test for the Difference Between Two Means
Hypothesized Difference	0
Level of Significance	0.05
Female Salary
Sample Size	21
Sample Mean	59330.80952
Sample Standard Deviation	53961.1581
Male Salary
Sample Size	19
Sample Mean	63553.68421
Sample Standard Deviation	77901.3926
Numerator of Degrees of Freedom	209817934130659000.0000
Denominator of Degrees of Freedom	6628920451792470.0000
Total Degrees of Freedom	31.6519
Degrees of Freedom	31
Standard Error	21402.3101
Difference in Sample Means	-4222.8747
Separate-Variance t Test Statistic	-0.1973
Two-Tail Test
Lower Critical Value	-2.0395
Upper Critical Value	2.0395
p-Value	0.8449

According to the above results, the P-value of the test is less than 5% level of significance, so the null hypothesis of the test gets rejected. Thus, it can be concluded that there is a significance difference between the average salary of male and female.

Conclusion

The male earns 68% of the total salary and male earns 32% of the total salary. The total number of female employees is 461 and the male employees is 539. The average salary of a female employee is $31768.51 and for the male employee is $57830.74. The maximum salary of a female employee is $308183 and the maximum salary of a male employee is $839840. The, total salary of a female employee is $14645283 and the total salary of a male employee is $31170769.

The Professionals get 15.80% of the total salary in which female earn 7.70% and male earn 8.10%. The Professionals get 15.80% of the total salary in which female earn 7.70% and male earn 8.10%. The Clerical and Administrative Workers get 11.80% of the total salary in which female earn 9.20% and male earn 2.60%. The Technicians and Trades Workers get 10.20% of the total salary in which female earn 1.60% and male earn 8.60%.

The study from the provided data from Australian Taxation Office (ATO) indicates that the proportion of machinery operators and drivers who are male is more than 80%, and there is a difference in salary amount between gender.

The study from the sample survey of 40 employees indicates that there is a significance difference between the average salary of male and female.

Most of employees not listed their occupation otherwise it is not specified which is 21.20% of the total salary. So, the Australian Taxation Office (ATO) should collect the data for each occupation which will be helpful in the further study of salary analysis.