Statistics problem, need help with answer and detailed on how to solve

A researcher at SRVMC wishes to try three different techniques to lower the blood pressure of individuals diagnosed with high blood pressure.  The subjects are randomly assigned to three groups.

Group 1 takes medication

Group 2 exercises

Group 3 follows a special diet. 

After four weeks, the reduction in each person’s blood pressure is recorded.  At an alpha level of significance of 0.05, the researchers now must test the claim that there is no difference among the means.

Is he correct?  Run the appropriate test to determine if he is correct.