Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 36 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 80 of the 97 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinaceal 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? OA. Ho: P₁ = P₂ H₂: P₁ P₂ OD. Hg: P₁ P₂ H₂: P₁ P₂ Identify the test statistic. (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 b. Test the claim by constructing an appropriate confidence interval. The 95% confidence interval is <(P₁-P₂) < (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? 0, there c. Based on the results, does echinacea appear to have any effect on the infection rate? Because the confidence interval limits OB. Ho: P₁ = P₂ H₁: P₁ P₂ OE. Ho: P₁ P₂ H₁: P₁ P₂ the null hypothesis. There sufficient evidence to support the claim that echinacea treatment has an effect. appear to be a significant difference between the two proportions. There OA. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate. OB. Echinacea does not appear to have a significant effect on the infection rate. OC. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate. OD. The results are inconclusive. OC. Ho: P₁ = P₂ H₁: P₁ > P₂ OF. Ho: P₁ #P₂ H₁: P₂ = P₂ evidence to support the claim that echinacea treatment has an effect.