please show your final calvulatations

A researcher wants to know if there is a difference between the mean amount of sleep that people get for various types of employment status. The table below shows data that was collected from a survey. Use the R window to answer the question below: dat =$(5.7,5.8,6.3,5.5,5.9,5.6,4,4.8,4,4.9,4.1,4.6,4, 4,9,8.4,9,8.7,8.8), catagory = c("Unemployed", "Unemployed", "Unemployed", "Unemployed", "Unemployed", "Unemployed", "Part Time Worker", "Part Tme Worker", "Part Time Worker", "Part Time Worker", "Part Tine Worker", "Part Time Worker", "Part Time Worker", "Part Time Worker", "Full Time Worker", "Full Time Worker", "Full Time Worker", "Full Time Worker", "Full Tine Worker") ) 11 brary (car) dat