At Oxford Company plants, thousands of boxes of cereal are filled during each eight-hour shift. As the operations manager of the plant, you are in charge of monitoring the amount of cereal contained in the box. Boxes are supposed to contain, on average, 368 grams of cereal as indicated on the package label. Because of the speed of the process, there is variation in the cereal weight form box to box causing some boxes to be underfilled and some overfilled. Moreover, if the process is not working properly, the average weight in the boxes could deviate too far from the label weight of 368 grams to be acceptable. Because it is too time consuming, costly and inefficient to weigh every single box, you must take a sample of boxes and make a decision regarding the likelihood that the cereal filling process is working properly. Each time a sample of boxes is selected and individual boxes are weighed, a sample mean is calculated. You need to decide the likelihood that such a sample mean could have been randomly drawn from a population whose true mean is 368 grams. Please try to solve the following questions

1. The Oxford Cereal Company wants to determine whether the cereal filling process is working properly (that is, whether the mean fill per box throughout the entire packaging process remains at the specified 368 grams and no corrective action is needed). To evaluate the 368 grams requirement, a random sample of 35 boxes is taken, each is weighted, and then the difference between the sample statistic and hypothesized population parameter is evaluated by comparing the mean weight (in grams) from the sample to the expected mean of 368 grams specified by the company. Please specify the null hypothesis and alternative hypothesis

1. The weight of 35 sample cereal boxes listed below and the population standard deviation is assumed to be 15 grams. Please identify whether the average amount filled was different from 368 grams. Alpha level =0.05 (please use confidence interval approach, critical value approach and P vale approach)

375,365,355,360,345,367,368,375,374,375,364,368,355,369,367,355,354,369,375,378,378,374,375,374,375, 375,365,355,360,345,367,368,375,374,375