Question: (6 points) Your company purchases rubber washers. It is extremely important that the diameter of the hole in the middle of the washer be no different than 0.5 inch. If it is different, the shipment must be returned to the manufacturer. You have just received a shipment of 10,000 washers. There's no way to measure the entire population, so you take a random sample of 35 of them. The sample mean diameter is 0.45 inches, and the standard deviation is calculated to be 0.12 inch. Given this information, is there evidence to suggest that the mean diameter of the entire shipment is something other than what it should be? Use the .05 level of significance to make your decision.

Using plain language, interpret your statistical decision. Be sure to state whether the shipment should be returned to the sender.