You are the manager of a production company. The production manager comes to you with the idea to change an old laser machine in your plant with a new one, and he claims that the new one will increase the performance of the production process. You asked him to record the cutting time in seconds for each item with the new and the old machine. The production manager reported the following results in seconds for one cut: New machine Old machine 42.1 41.3 42.4 43.2 41.8 42.7 43.8 42.5 43.1 44.0 41.0 41.8 42.8 42.3 42.7 43.6 43.3 43.5 41.7 44.1 a) Construct the 95% confidence intervals for the differences of the means. b) Do you believe that the new machine increased the performance of the company and do you plan to allow the production manager to buy the new machine