In a well-functioning labor market, individuals with same productive attributes (e.g. education attainment, working experience) should be equally paid. The existence of public-private pay gap for individuals with similar productive characteristics thus has implications for efficiency and equity in the labour market. For instance, this implies that employees in the public sector receive rents at the cost of tax payers, and the private sector activities may be crowded out as it becomes hard to retain employees.
You have been appointed by the Australian Productivity Commission to analyse the public-private pay gap in Australia. The data are drawn from the 2017 HILDA (Household, Income and Labour Dynamics in Australia) survey. Using the tools learned in your current Business Statistics course provide the Commission with an analysis of the public-private pay gap. You may assume the Commission members have a good understanding of basic statistics. In addition, the Commission would like you to prepare a ministerial brief to illustrate the key findings of your analysis to the Minister for Employment, Skills, Small and Family Business.
There are two parts to this assignment, each described in detail below:
Part A (3 + 2 + 3 + 3.5 + 3.5 + 3 + 3.5 + 2.5 = 24 marks; professional report = 8 marks)
Locate the data file on CANVAS. Use the 5% significance level and the 95% confidence level where relevant.
Focusing on the variable wage for the public sector employees only for this question: as shown in several lectures there are two distinct methods of calculating summary or descriptive statistics using Excel. This question requires you to use both methods. First use Excel Data Analysis Tool Pack (the descriptive statistics option) to calculate and interpret the summary statistics. Second use Excel to calculate all descriptive statistics documented in your report. These calculations should be carefully laid out in Excel and should NOT use any hard-wired Excel statistical functions e.g. Average, Median, Mode, STDEV et al. You can use the Excel sort command, the sum command, and any other non-statistical excel commands.
Repeat step 1 above for the variable wage for the private sector employees.
Draw a histogram of the wage distribution for the public and private sector employees respectively. Interpret the graphs carefully.
What are the main differences in demographic and social-economic characteristics between employees in the public and private sector? Aid your answer with appropriate tables/graphs.
Propose a statistical method to estimate the mean hourly wage rate for all public sector employees and all private sector employees, respectively. Clearly label your diagram and indicate any assumptions made and explain carefully.
A media report claims that the mean hourly wage rate for all public sector employees in Australia in 2017 was 49 AU$. Do you agree? Perform a hypothesis test at the 5% significance level. Clearly label your diagram and indicate any assumptions made. Explain carefully if any potential errors in your decision making.
Since the data file (AssignmentBusStats.xls) suggests a higher mean hourly wage rate in the public sector, a researcher hence concludes that the population mean hourly wage rates are not equal between two sectors. Do you agree? Propose a statistical method to examine if the population mean hourly wage rates are equal for the public and private sector. Clearly indicate any assumptions made.
Should the Minister be concerned if the population mean hourly wage rate is higher in the public sector?
Part B: Write a ministerial brief of no more than 200 words containing no more than 3 graphs on the public-private pay gap in Australia and any other interesting findings that would be of policy relevance to the Minister. Draw on the relevant evidence you have gathered from Part A, as well as other information/evidence not covered here but you believe is useful. Your brief should summarize your results from part A in a non-technical way and provide relevant conclusions (8 marks).
