A manufacturer of small electric motors used in heat pump claims that the motors average 450 hours of use before their first breakdown.  A major heat pump manufacturer (the customer) has suggested to the manufacturer that their motors are performing much better than their claim. As the Engineering Intern hired by the electric motor manufacturer you have been asked to investigate whether or not the heat pump manufacturer (the customer) has a legitimate case. To address the problem, you took a sample of 64 of these motors. Your analysis showed an average of 460.5 hours of use before a breakdown, with standard deviation of 20 hours.

a) Develop a hypothesis to investigate this problem based on the claim of the heat pump manufacturer (the customer) with α= 0.01.  What is your decision or recommendation at α = 0.01

b) Will your decision or recommendation change at α = 0.05?