As shift manager at a local fast food place, you are responsible for ensuring quality control. You do not want to weigh all the frozen hamburger patties that get delivered by your supplier to make sure they weigh four ounces on average, so you choose 100 patties at random. You calculate that the sample mean weight of patties is 2.6 ounces and the standard deviation of the weight of hamburger patties to be 0.4 ounces. You tell your employee to choose 36 patties at random and find the average weight. Required:
For what values would you tell your employee to reject the shipment, if you wanted the probability of a type I error to be 0.10 or less?