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2. A manufacturing company wants to reduce the amount of wasted material in the manufacturing process employed by their factories. Suppose their current manufacturing process results in an average of 134 kg/ day of wasted material at each of their factories. A team of engineers and operations research specialists proposes modifications to the manufacturing process that they claim will reduce wasted material (on average). To test this new process, the company implements it at one of their factories and records the amount of wasted material (in kg) each day for 10 days. The sample mean of the daily waste at the factory implementing the modified manufacturing process over the course of this experiment is 120.7 kg. Assuming the amount of wasted material each day at the factory represents a random sample from a normal distribution, evaluate the evidence concerning whether the proposed modifications to the manufacturing process are effective at reducing waste (on average) as follows: (a) State the parameter of interest and null and alternative hypothesis for this experi- ment. (3 pts) (b) It is known that, under the current manufacturing process, the standard deviation of daily wasted material at each factory is 14.6 kg. Assuming that the standard deviation of daily wasted material at each factory will not change under the proposed modifications, test whether the modifications were effective at reducing waste at the a = .05 significance level. Report a p-value and interpret your results. (4 pts) 3 (c) The team that proposed the modifications claims that the modifications should reduce waste by 17 kg/day on average. Assuming this claim is accurate, what is the power of the test you performed in (b)? (4 pts) (d) Determine a 95% confidence interval for the mean daily waste at the factory under the newly modified process (assume the same standard deviation as in (b)). At the o = 05 significance level, is the team's claim from (c) of a reduction of 17 kg/day on average reasonable? (4 pts)