A team of psychologists designed a study in which 12 psychiatric patients diagnosed as having generalized anxiety disorder were randomly assigned to one of three new types of therapy, here labeled X, Y, and Z. One year after therapy, the patients' overall mental health scores were as follows:

Mental Health Assessment:

Therapy X    Therapy Y     Therapy Z
85                    78                 79
79                    81                 83
84                    68                 75
67                    75                 74

Do these results suggest that the different therapies have different effects on mental health?

(Use the .05 level.)

a. Use the five steps of hypothesis testing.

b. Sketch the distribution involved.

c. Explain your results.