In a study of treatments for very painful "cluster" headaches, 153 patients were treated with oxygen and 140 other patients were given a placebo consisting of ordinary air. Among the 153 patients in the oxygen treatment group, 120 were free from headaches 15 minutes after treatment. Among the 140 patients given the placebo, 32 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. 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? OA. Ho: P1 = P2 OB. Ho: P1 # P2 O C. Ho: P1 =P2 Hy : P 1 > P2 H1 : P1 = P2 H1 : P1 # P2 OD. Ho: P1 = P2 OE. Ho: P1 = P2 OF. Ho: P1 2 P2 H1: P1 = P2 H1 : P1 7 P2 Hy : P1 # P2 Identify the test statistic. z= (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 the significance level of a = 0.05, so the null hypothesis. There evidence to support the claim that the cure rate with oxygen treatment is higher than the cure rate for those given a placebo. b. Test the claim by constructing an appropriate confidence interval. The 90% confidence interval is | = (P1 - P2)