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Rhino viruses typically cause common colds. In a test of the effectiveness ofechinacea, 33 of the 40 subjects treated with echinacea developed rhinovirus infections. In a placebogroup, 97 of the 114 subjects developed rhinovirus infections. Use a 0.05 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 hypothesistest?

Identify the test statistic.

z=

Identify theP-value.

P-value=

What is the conclusion based on the hypothesistest?

TheP-value is the significance level of = 0.05, 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 95% confidence interval is _____ < (p1-p2) < ____.

What is the conclusion based on the confidenceinterval?

Because the confidence interval limits ______ 0, there _______ appear to be a significant difference between the two proportions. There ______ evidence to support the claim that echinacea treatment has an effect.

c. Based on theresults, does echinacea appear to have any effect on the infectionrate?

Choose the correct answer.

A. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.

B. Echinacea does not appear to have a significant effect on the infection rate.

C. Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.

D. The results are inconclusive.