Qmth104 Quantitative Methods | Ethics Assessment Answers

Business reports are practical learning tasks where students apply the theories they have been studying to real world situations. The students are required to select a topic, collect information (Primary and/or secondary) and prepare a report describing a business problem or incident.

1. Understand ethics and ethical behaviour in undertaking a statistical study.
2. Interpret data by using descriptive statistics.
3. Explain probability, probability distributions and their applications in decision making.
4. Explain the concepts of statistical inference and its application.
5. Interpret results and make decisions through the use of appropriate statistical techniques.

Describe the dataset and describe each of the variables For each variable answer the question is it categorical or numerical?

Discuss what you learnt after thinking about the previous sections.

Introduction

This study sought to investigate whether there is significant differences in the salaries of the female and male respondents. The question we sought to answer was “Is there evident that the starting salaries of the males and the females are different?” Previous studies have tried to argue that the females are disadvantage when it comes to the salaries they receive when compared to their male counterparts (Correll, et al., 2007). The population is the fresh graduates within Sydney who got employed in the last 2 years. There has been talk of wage gap between the males and the females of the same level (Blau & Kahn, 2007). The dataset collected is given below;

Table 1: Dataset

Where 1 = Marketing, 2 = Finance, 3 = Technical services and 4 = Research

Description of the data set

The data set presented in table 1 above consists of three variables. Two of the variables are categorical variables while one of the variables is a numerical variable (Fay & Proschan, 2010). The categorical variables are gender and department while starting salary is the numerical variable. There are a total of 30 observations in the dataset.

Summary of the data set

Figure 1 below gives a pie chart of the gender. It can be seen that majority of the respondents were male respondents (60%, n = 18). Female respondents were represented by 40% (n = 12)

In terms of department in which the respondents belong to. Majority were in the technical services department (40%, n = 12), research were represented by 33.3% (n = 10). The department that had few representation was marketing (6.7%, n = 2) while finance had 20% (n = 6) representation (John, 2006).

Figure 2: Bar graph of department

Table 2: Descriptive statistics

On average, the annual starting salary for the fresh graduates is $39,698.4 with the starting salary for a fresh graduate being $69,600 while the lowest being $32,640. The median salary for the sample is $36,600 with the mode (most frequent income) being $36,600 (same amount as the median starting salary).

Confidence intervals

An independent samples t-test was performed to compare the mean starting salary for the fresh graduate among the female group and the male group (Derrick, et al., 2017). Results showed that the mean starting salary for the fresh graduate among the female group (M = 43670.00, SD = 15316.85, N = 12) was not significantly different from the male group (M = 37050.67, SD = 4397.22, N = 18), t(28) = 1.742, p > .05, two-tailed. The difference of 6619.33 scale units indicated an insignificant effect, and the 95% confidence interval around the difference between group means was (-1162.30 to 14401.00).

95% confidence interval

Lower Limit:

Upper Limit:

From this, we are 95% confident that the true mean starting salary of the population under study is between $35760.754 and $43,636.046.

Conclusion

This study sought to investigate whether the starting salary for the fresh graduates in Sydney differ between the male and the female groups. A sample of 30 respondents was used to test the claim that the average starting salary for the fresh graduates is different between the males and the females. The respondents came from four different departments namely, finance, technical services, research and communication. An independent t-test with 95% confidence interval was conducted to test the claim.

On average, the annual starting salary for the fresh graduates is $39,698.4 with the starting salary for a fresh graduate being $69,600 while the lowest being $32,640. Results showed that there is no significant difference between the starting salaries for the males and the females. That is, the starting salary for the males is not significantly different from the starting salary of the females despite the fact that the female respondents slightly earned more as compared to the male respondents.

References

Blau, F. D. & Kahn, L. M., 2007. The Gender Pay Gap. The Economists, 4(4).

Correll, S. J., Benard, S. & Paik, I., 2007. Getting a Job: Is There a Motherhood Penalty?. American Journal of Sociology, 112(5), p. 1297–339.

Derrick, B., Toher, D. & White, P., 2017. How to compare the means of two samples that include paired observations and independent observations. The Quantitative Methods for Psychology, 13(2), p. 120–126.

Fay, M. P. & Proschan, M. A., 2010. Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules.

John, A. R., 2006. Mathematical Statistics and Data Analysis.