It is known that the time to complete a certain task at the manufacturing process is normally distributed with a mean of 35 minutes. If a random sample of 20 workers has the average time of 33.1 minutes to complete the task with the standard deviation of 4.3 minutes, test the hypothesis, at the 0.05 level of significance, that = 35 minutes against the alternative that < 35 minutes. Show all our work.