In a study of treatments for very painful "cluster" headaches, 160 patients were treated with oxygen and 146 other patients were given a placebo consisting of ordinary air. Among the 160 patients in the oxygen treatment group, 114 were free from headaches 15 minutes after treatment. Among the 146 patients given the placebo, 32 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? O A. Ho: P₁ = P2 OB. Ho: P₁ = P2 H₁: P₁ P2 OC. Ho: P₁ P2 H₁: P₁ = P2 H₁: P₁ P₂ O D. Ho: P₁ P₂ O E. Ho: P₁ P₂2 H₁: P₁ P2 OF. Ho: P₁ P2 H₁: P₁ P₂ H₁: P₁ P₂ Identify the test statistic. Z= z=0 (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is ✔ evidence to support the claim that the cure rate with the significance level of a = 0.01, so oxygen treatment is higher than the cure rate for those given a placebo. b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is < (P₁-P₂) <. (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? Because the confidence interval limits include Because the confidence interval limits values, it appears that the cure rate is ▼0, it appears that the two cure rates are for the oxygen treatment than for the placebo. c. Based on the results, is the oxygen treatment effective? OA. The results suggest the oxygen treatment is effective in curing "cluster" headaches. OB. The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rates appear to be the same. O C. The results suggest that the oxygen treatment is not effective in curing "cluster" headaches because the cure rate for the oxygen treatment appears to be lower than that of the placebo. O D. The results are inconclusive. the null hypothesis. There