STATISTICS

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?