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 counterfeits, which bear the proper markings for this grade of bolt, but are made from the inferior materials. for this application, the genuine bolts are known to have a tensile strength that is normally distributed with a mean of 1400 pounds and a standard deviation of 30 pounds. the mean tensile strength for the bolts tested is 1385 pounds.

A) formulate and carry out a hypothesis test to examine the possibility that the bolts in the shipment might not be genuine

B) if she wants to find a 97% confidence interval of width no more than 20 pounds, what sample she required to take

C)find the power of the test at u=1380