Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 36 of the 41 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 96 of the 113 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? A. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 B. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 C. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 D. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 E. Upper H 0​: p 1greater than or equalsp 2 Upper H 1​: p 1not equalsp 2 F. Upper H 0​: p 1less than or equalsp 2 Upper H 1​: p 1not equalsp 2 Identify the test statistic. zequals nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) What is the conclusion based on the hypothesis​ test? The​ P-value is ▼ greater than less than the significance level of alphaequals0.01​, so ▼ reject fail to reject the null hypothesis. There ▼ is 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 99​% confidence interval is nothingless thanleft parenthesis p 1 minus p 2 right parenthesisless than nothing. ​(Round to three decimal places as​ needed.) What is the conclusion based on the confidence​ interval? Because the confidence interval limits ▼ include do not include ​0, there ▼ does does not appear to be a significant difference between the two proportions. There ▼ is not 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 appear to have a significant effect on the infection rate. There is evidence that it lowers 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 increases the infection rate. D. The results are inconclusive. Click to select your answer(s).

Answer 1