Question: Patients suffering from a certain disease have three treatment options available. Twelve patients suffering from the disease were randomly assigned to one of the three treatment options, and the recovery time in weeks was noted. The results are provided in the following table:

Time recovery (Weeks)

Treatment A Treatment B Treatment C

3 7 4

8 6 3

9 5 2

7 5 6

Assuming the necessary assumptions are satisfied, can it be concluded, at the 5% level of significance, that not all mean recovery times are equal? Formulate the test the appropriate hypotheses. Use the critical value approach.