Do you agree? Propose a statistical method to examine whether the researcher’s statement is true or not. Clearly indicate any assumptions made. Should the Minister be concerned that the population mean hourly wage rate is higher in the public sector?

You have been appointed by the Australian Productivity Commission to analyse the public-private pay gap in Australia. The data are drawn from the 2019 HILDA 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 that 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.
Part A:
The Australian government would like to have a rough idea about the mean hourly wage rate for both sectors. Propose a statistical method to estimate the mean hourly wage rate for public sector employees and private sector employees, respectively. List any assumptions made and carefully explain your findings.
Since the data file suggests a higher mean hourly wage rate in the public sector, a researcher hence states that the population means hourly wage rates for public and private sectors are different. Do you agree? Propose a statistical method to examine whether the researcher’s statement is true or not. Clearly indicate any assumptions made.
Should the Minister be concerned that the population mean hourly wage rate is higher in the public sector?

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