401077 Biostatistics Assignment 2: Income, Education, and Gender Study

This assignment presents a comprehensive analysis of a dataset concerning full-time workers in Sydney, Australia. The analysis begins with an investigation into whether average self-reported weekly income differs between male and female workers, employing both t-tests (on both raw and log-transformed income data) and non-parametric Mann-Whitney tests to address the research question. The student justifies the choice of tests based on data distribution characteristics and presents the results using the 5-step method. The second part of the assignment focuses on calculating and interpreting descriptive statistics, specifically the mean and standard deviation of self-reported work hours, constructing a 95% confidence interval, and determining the margin of error. The assignment also requires the estimation of the minimum sample size needed to achieve a specified margin of error for a confidence interval. The final section examines the relationship between highest educational qualification and gender, using a two-way contingency table and a chi-square test of independence. The student calculates proportions and addresses the minimum sample size required to detect differences in proportions between genders. The provided R code is also included in the appendix.