In a study of treatments for very painful"cluster" headaches, 159 patients were treated with oxygen and 156 other patients were given a placebo consisting of ordinary air. Among the 159 patients in the oxygen treatmentgroup, 107 were free from headaches 15 minutes after treatment. Among the 156 patients given theplacebo, 31 were free from headaches 15 minutes after treatment. Use a 0.05 significance level to test the claim that the oxygen treatment is effective. Complete parts(a) through(c) below. Find the null and alternative hypothesis, test statistic, p value, conclusion, confidence interval, and confidence interval conclusion.