Assignment Task:
PART 1
Economists often discuss how women earn less than men on average as women often choose to work less hours. Researchers suggest that the choice of hours worked depends on various factors such as age, childcare needs, occupation choice and flexibility. In order to investigate the relationship between the hours worked and the income of Australian men and women, a researcher plans to survey a sample of individuals across the country. Answer the following questions:
1. What type of survey method the researcher could use and why?
2. What sampling method could be used to select the sample and why?
3. What are the variables the researcher should consider collecting data for the purpose of the analysis and why? Identify the data type(s) for the variables. (1.5 marks)
4. What kind of issues we may face in this data collection?
PART 2
Suppose a researcher has collected data form a sample of 60 individuals using the sampling method you have proposed in (b). For each individual, the hours worked per week and yearly income (measured in ‘000’s dollars) were recorded. The data are stored in the file named “ASSIGNMENTDATA.XLS” in the course website. Using EXCEL, answer the following questions:
5. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, smallest and largest values and the three quartiles, for each variable.
6. Using the appropriate BIN values, draw a histogram for each variable. Then, comment on the shape of the two distributions.
7. Use an appropriate plot to investigate the relationship between the two variables. Identify the dependent and independent variable and explain your choice
8. Compute a numerical summary measure to measure the strength of the linear relationship between the two variables. Interpret this value.
9. Construct a 90% confidence interval estimate for the population average yearly income.
Interpret the interval (use the spreadsheet on the course website).
10. Test the hypothesis that population average hours worked per week is less than 30 hours.
Use a 5% level of significance (use the spreadsheet on the course website).
11. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
12. Interpret the coefficient of determination, R-squared (R2) value.
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