Before accepting a large shipment of bolts, the director of an elevator construction project checks the tensile strength of a simple random sample consisting of 20 bolts. She is concerned

that the bolts may be counterfeit, meaning that they are made of inferior materials. For this application, the genuine bolts are known to have a tensile strength that is normally distributed with a mean of 1450 pounds with a standard deviation of 35 pounds. The mean tensile strength for the bolts in the sample is 1370 pounds. Given a level of significance of 0.025, formulate and carry out the steps of a hypothesis test to examine the possibility that the bolts in the shipment might not be genuine.