Question: A cup of coffee is found to have only 72.8 milligrams of caffeine. Test (at the 5% level) whether the beans used could have come from the same population as those that generated the data in problem.
Problem: The amount of caffeine (milligrams) in randomly sampled cups of coffee was as follows:
112:8, 86:4, 45:9, 110:3, 100:3, 93:3, 101:9, 115:7, 92:5, 117:3, 105:6, 81:6
a. Find the one-sided 99% confidence interval for the population mean caffeine content of a cup of coffee that claims "at least...."
b. Find the one-sided 99% prediction interval for the caffeine content of the next cup of coffee, again claiming "at least...."