"Frontier medicine" is a term used to describe medical therapies (e.g., energy healing, therapeutic prayer, spiritual healing) for which there is no plausible explanation. The Lancet (July 16, 2005) published the results of a study designed to test the effectiveness of two types of frontier medicine-music, imagery, and touch (MIT) therapy and therapeutic prayer-in healing cardiac care patients. Patients were randomly assigned to receive one of four types of treatment: (1) prayer, (2) MIT, (3) prayer and MIT, and (4) standard care (no prayer and no MIT). Six months after therapy, the patients were evaluated for a major adverse cardiovascular event (e.g., a heart attack). The results of the study are summarized in the accompanying table.

a. Identify the two qualitative variables (and associated levels) measured in the study.
b. State H0 and Ha for testing whether a major adverse cardiovascular event depends on type of therapy.
c. Use the MINITAB printout on p. 794 to conduct the test mentioned in part b at a = .10. On the basis of this test, what can the researchers infer about the effectiveness of music, imagery, and touch therapy and the effectiveness of healing prayer in heart patients?

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Number of Patients with Major Cardiovascular Events Number of Patients with No Events Therapy Prayer 43 47 39 50 139 182 MIŤ Prayer and MIT 138 150 189 192 142 Standard