The article “Effects of Pulmonary Rehabilitation on Exercise Capacity and Disease Impact in Patients with Chronic Obstructive Pulmonary Disease and Obesity” (Physiotherapy 2018: 248–250) reports a study in which 155 COPD sufferers completed an eight-week pulmonary rehabilitation program at St. James’ Hospital in Dublin Ireland. Before and after the program, subjects performed the Six-Minute Walk Test (6MWT), which simply measures the distance (in meters) patients can walk in six minutes. The accompanying table summarizes the increase in 6MWT distance for the participants (i.e., post-rehab distance minus pre-rehab distance), separated by their weight category.

a. Does the data suggest that the pulmonary rehab program is not equally effective for COPD patients of all weight categories? State and test the relevant hypotheses at significance level .05.
b. Investigate differences between weight categories with respect to mean increase in 6MWT distance.

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Weight category Underweight/normal Overweight Obese n 53 39 63 Mean 61 67 41 SD 80 86 87