HW Problem 49. (5 pts) A manufacturing firm which produces specialty rods wants to pick the machine which produces them the most consistently (i.e. with the least variability). The owner is considering the purchase of a new machine. However, before he spends the money on the new machine, he wants to be certain that the variability of the output on the new machine is any different than the variability of the output on his existing machine. He randomly selects 20 specialty rods produced by his existing machine which yields a sample mean diameter of 9 millimeters with a sample standard deviation of 4.15 microns. 22 rods produced by the new machine result in a sample mean diameter of 9 millimeters with a sample standard deviation of 2.1 microns. At the .01 level of significance, test to see if the variance of output is different for the two machines. List and clearly label all eight steps.