Question: Fuel Consumption and Cars The joint venture ContiTechJiebao Power Transmission Systems Ltd. produces many makes and models of automobile drive belts. One popular poly V-belt is designed to have length 1050 mm. To ensure that the belts meet this specification, 18 are randomly selected from the assembly line every hour and carefully measured. If there is any evidence that the population mean length is different from 1050 mm, the entire line is shut down for inspection.
a. Assume the distribution of belt lengths is normal and σ = 3.7 mm. In a two-sided hypothesis test of H0: μ = 1050 versus H0: μ = 1050, find the critical values in the X¯ world. Use a = 0.01.
b. In a sample of 18 belts, suppose x¯ = 1049. Should the assembly line be shut down? Justify your answer using the Z distribution and the appropriate X distribution.