Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 35 of the 41 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 81 of the 98 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 hypothesis​ test?

identify the test statistic, p-value .

What is the conclusion based on the hypothesis​ test?

The​ P-value is less than or greater than the significance level of alpha =0.05​, so reject

or fail to reject the null hypothesis. There is or is not 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-p 2)<_.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits do not include or include ​0, there does not or does appear to be a significant difference between the two proportions. There is not or is evidence to support the claim that echinacea treatment has an effect.

c. Based on the​ results, does echinacea appear to have any effect on the infection​ rate?

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

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

Answer 1

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