Question: Caffeine Content

A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per 5 ounces. You work for a consumer agency and are asked to test this claim. You find that a random sample of 42 five-ounce servings has a mean caffeine content of 83 milligrams and a standard deviation of 35 milligrams.

a) At a 5% level of significance, do you have enough evidence to reject the shop’s claim?

• Perform the appropriate statistical test.

• Show your work for this test, state your conclusion, and explain your answer.

b) Create a 99% confidence interval for the mean caffeine content of this shop’s coffee drinks.