In a study of treatments for very painful​ "cluster" headaches, 141 patients were treated with oxygen and 153 other patients were given a placebo consisting of ordinary air. Among the 141 patients in the oxygen treatment​ group, 115 were free from headaches 15 minutes after treatment. Among the 153 patients given the​ placebo, 22 were free from headaches 15 minutes after treatment. Use a 0.01 significance level to test the claim that the oxygen treatment is effective. Complete parts​ (a) and​ (b) below.

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.