(a)An electrical appliances manufacturing company produce light bulbs that have a lifetime that is approximately normally distributed with a mean of 600 hours and a standard deviation of 30 hours. Test the hypothesis that = 600 hours while the alternative, 600 hours, if a random sample of 20 bulbs has an average life of 698 hours.

(b)A company claims that the average stretchable strength of yarn A exceeds the average stretchable strength of yarn B by at least 10 kilograms. To test this claim, 40 pieces of each type of yarn were tested under similar conditions. Type A yarn had an average stretchable strength of 76.7 kilograms with a standard deviation of 5.28 kilograms, while type B yarn had an average stretchable strength of 87.8 kilograms with a standard deviation of 4.61 kilograms. Test the company's claim using a 0.01 level of significance.