A machine manufactures bolts that are supposed to be 3 inches in length. Each day a quality engineer selects a random sample of 50 bolts from the day's production measures their lengths, and performs a hypothesis test of H : μ=3 versus H1: μ#3 , where μ is the mean length of all the bolts manufactured that day. If He is rejected at the 5% level (or, =0.05), the machine is shut down and recalibrated. a. [35 points] If the sample mean is x = 3.011 inches and the sample standard deviation 0.0 inches, show and NUMBER all 5 steps of the hypothesis- testing procedure (in the handout) to decide whether or not the machine needs to be recalibrated. Include the case (l, ll, lll or IV) that appropriately categorizes the situation described in step 3. Also, state whether or not you are using the central limit theorem in step 3.