(a) The Production Manager of Mechtex Ltd., a manufacturer of machines, is investigating a claim by customers about machine A and machine B that it manufactures. The claim is that machine A has a longer useful life than machine B. A sample of 60 machine As taken from the market reveals that the machine has a mean useful life of 28,000 hours with a standard deviation of 900 hours. A sample of 80 machine Bs has a mean useful life of 30,000 hours with a standard deviation of 1,000 hours. Required: Advise the Production Manager of Mechtex Ltd. if there is a significant difference in the useful lives of the machines. Use a significance level of 5%. (8 marks)