$4.$ Sacramento County conducts a training program to improve recruitment performance. Data is collected to track the number of days to fill open positions before and after the training. A sample of $15$ positions before the training and a different sample of $20$ positions after the training are selected for analysis. Using the data in the file named $$Dataset $4,$ conduct a hypothesis test$($s$)$ to assess if the training improves the recruitment performance of the human resources department.