What is the mean income in the two sectors? Conduct a two-sample t-test for the difference in income between the two sectors. Give the 95% confidence interval for the difference in incomes between the two sectors, and the p-value of your test.

This section involves a detailed examination of financial data related to registered charities and non-profits in Ireland, a sector that remains relatively underexplored despite its significant monetary transactions (approximately €13 billion annually).

Benefacts, founded in 2015 as another charitable entity, plays a vital role in compiling comprehensive data and fostering transparency within the sector. A notable contribution by Benefacts is the `benefacts.csv` dataset, accessible via the `Assessment` section on our Blackboard site.

Refer to the accompanying data dictionary to understand variable descriptions. Additionally, consult the `sectors.pdf` document to identify the specific charitable sectors assigned to your group.

Focus your analysis on the 2019 financial year and the designated sectors outlined in `sectors.pdf`. Begin by examining income distributions within these sectors, calculating the mean income and identifying the number of observations.

Subsequently, conduct a two-sample t-test to assess income differences between the assigned sectors. Provide a 95% confidence interval for this difference and report the corresponding p-value. Clearly state your hypothesis for this statistical comparison.