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.
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.
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