Patients with painful knee osteoarthritis were randomly assigned in a clinical trial to one of five treatments: glucosamine, chondroitin, both, placebo, or Celebrex, the standard therapy. One outcome recorded was whether or not each patient experienced substantial improvement in pain or in ability to function. The data are given in the following table.

(a) Use a chi-square test to compare the success rates at α = 0.05. (The value of the chi-square statistic is χ2s = 9.29.)
(b) Verify the value of χ2s given in part (a).

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Successful outcome Treatment Sample size Number Percent Glucosamine 317 Chondroitin Both Placebo Celebrex 318 317 313 318 192 202 208 178 214 60.6 63.5 65,6 56.9 67.3