A large horse riding manufacturer, Buford Hats, is concerned that the mean weight of their classic riding hat is not greater than 2.75 pounds. It can be assumed that the population standard deviation is .5 pounds based on past experience. A sample of 350 hats is selected and the sample mean is 2.86 pounds. Using a level of significance of .01, is there evidence that the population mean weight of the hats is greater than 2.75 pounds? Fully explain your answer.