In a study of treatments for very painful “cluster” headaches, 148 patients were treated with oxygen and 155 other patients were given a placebo consisting of ordinary air. Among the 148 patients in the oxygen treatment group, 115 were free from headaches 15 minutes after treatment. Among the 155 patients given the placebo, 25 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) through (c) below.
a. Test the claim using a hypothesis test. Consider the first sample to be the sample of patients treated with oxygen and the second sample to be the sample of patients given a placebo. What are the null and alternative hypotheses for the hypothesis test?
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, is the oxygen treatment effective?