An important manufacturing procedure produces cylindrical components for automotive industry. It is significant that the procedure produces parts having mean of 5.0 millimeters. The engineer involved conjectures that population mean is 5.0 millimeters. An experiment is conducted in which 100 parts produced by process are chosen randomly and the diameter measured on each. It is known that the population standard deviation ? = 0.10. The experiment points out a sample average diameter x-bar = 5.025 millimeters. Does this sample information appear to support the engineer's conjecture? (Prove your answer).