Rhino viruses typically cause common colds. In a test of the effectiveness of Echinacea, 40 of the 45 subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections. We want to use a 0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, does Echinacea appear to have any effect on the infection rate?
Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim.