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...

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). Suppose that the sample of 25 cereal boxes indicates a sample mean (x ) ̅= 372.5 grams and the population standard deviation s is assumed to be 15 grams.

At the 0.05 level of significance, is there sufficient evidence that the mean fill is different from 368 grams?