A lending firm knows a financial application takes on average 12.8 minutes and has a standard deviation of 2.1 minutes. A project manager thinks that since he works with farmers the application will take longer to complete. He took a sample of 36 completed applications and found the average time was 13.4 minutes. The sample data is normally distributed. Use α = 0.05. Is he correct in his assumption?
Conduct a full hypothesis test for this problem.