Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 45 of the 52 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 81 of the 97 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis test? O A. HO: P1 = P2 OB. Ho: P1 2 P2 O C. Ho: P1 # P2 H1 : P1 > P2 Hy : P1 7 P2 H1 : P1 = P2 OE. HO: P1 = P2 OF. HO: P1 = P2 OD. Ho: P1 =P2 H1 : P1 = P2 H1 : P1 = P2 H1: 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 = 0.01, so the null hypothesis. There sufficient evidence to support the claim that echinacea treatment has an effect.b. Test the claim by constructing an appropriate confidence interval. The 99% confidence interval is |= (P1 - P2)