6.27 In order to shorten the cycle time of an assembly process, an industrial engineer has simpli- fied the operations and designed a new fixture. With the old method, the average time for assembly is 10 minutes. To test his claim an experiment is conducted in which 15 workers trained in the new method participate. (a) Set up the hypotheses to show that the average assembly time with the new method is less than 10 minutes. (b) Suppose that the sample mean for the 15 workers is 8.7 minutes. If o = 2 minutes, is there statistically significant evidence that the average time is reduced? Use a = .05. (c) The industrial engineer claims that the new method will reduce the average time by at least 1.5 minutes. What chance (power) does this experiment have of detecting the claimed improvement