Rhino viruses typically cause common colds. In a test of the effectiveness of ec

Question

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, 90 of the 104 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. H_0: p_1 = p_2 H_1: p_1 p_2 E. H_0: p_1 lessthanorequalto p_2 H_1: p_1 notequalto p_2 F. H_0: p_1 greaterthanorequalto p_2 H_1: p_1 notequalto p_2 Identify the test statistic. z = (Round to two decimal places as needed.)

Explanation / Answer

Here p1=x1/n1 = 36/42, p2=x2/n2 =90/104 and p=(x1+x2) /(n1+n2) =126/146.

The test statistic is,

z=(p1-p2) /sqrt(p(1-p)(1/n1 + 1/n2)) =((36/42)-(90/104))/sqrt[(126/146)(1-(126/146))((1/42)+(1/104))]

                                                                  = - 0.13 (Ans)

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