A researcher designed a study to examine the effects of calcium supplementation on bone density. She randomly assigned subjects to either receive no calcium supplementation, receive the ADA recommended dose of calcium supplementation, or to receive twice the ADA recommended dose of calcium supplementation. After 6 months, she measures the bone density of all subjects and she wants to compare the mean bone density of the three groups. She also wanted to examine if the effect of calcium supplementation on bone density was different between women under 50 years old and women over 50 years old. What statistical test would be best to study these questions?

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