A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.2 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, population mean, is greater than 7.2 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.5 ounces and that the standard deviation is 0.4 ounces. Based on this information, complete the parts below.

(a) What are the null hypothesis and the alternative hypothesis that should be used for the test?

(b) Suppose that BIG decides not to reject the null hypothesis. What sort of error might it be making? (select one: Type I or Type II

(c) Suppose the true mean amount of coffee dispensed by the machine is 7.2 ounces. Fill in the blanks to describe a Type I error. A Type I error would be select one: Rejecting/Failing to Reject the hypothesis that is Select one: less than/less than or equal to/greater than/greater than or equal to/not equal to/equal (Choose one) to Select one: 7.2/7.5/0.4 (Choose one) when, in fact, population mean, is Select one: equal to 0.4/equal to 7.2/less than 0.4/less than 7.2/greater than 7.2/greater than 7.5