Please answer all of the questions and show all calculations.

A drug manufacturer states that each capsule of their drug contains a mean (u) of 500 mg of the active ingredient. To test this claim, researchers collect a sample (n) of 25 capsules of the drug. They get the following data: sample mean = 490 mg and sample standard deviation (s) of 8.5 mg. Is the active ingredient in each capsule less than what the manufacturer claims?

Set a = 0.01 and run the appropriate hypothesis test(s).