Question

Rhinoviruses 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. Test the claim using a hypothesis test.

Group of answer choices

A.P value=0.572; fail to reject H₀

B.P value=0.508; fail to reject H₀

C.P value=0.605; fail to reject H₀

D.P value=0.501; fail to reject H₀

Answer 1

x1                =	40	x2                =	88
p̂1=x1/n1 =	0.8889	p̂2=x2/n2 =	0.8544
n1                       =	45	n2                       =	103
estimated prop. diff =p̂1-p̂2    =		0.0345
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.8649
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0611
test stat z=(p̂1-p̂2)/Se =		0.565
P value   =		0.5721

option A is correct

A.P value=0.572; fail to reject H₀