Rhinoviruses typically cause common colds. In a test of the effectiveness of ech

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 103 subjects developed rhinovirus infections. Construct a 95% confidence interval estimate of the difference between the two rates of infections. Does echinacea appear to have any effect on the infection rate? Also, use the data to test the claim that the echinacea treatment has an effect? If you were a physician would you recommend echinacea?

Explanation / Answer

Not sure whether you are supposed to use Wilson estimates (add one success and two trials to each proportion). I have done so here, if you aren't supposed to just redo the problem without them. p1 (experimental) =(40+1)/(45+2)=0.872 p2 (control)= (88+1)/(103+2)=0.848 Formula for standard error is sqroot{( p1*(1-p1))/(n1+2))+(p2(1-p2))/(n2+2))} Calculating standard error using this formula we get SE=0.06 At 95% z* is 1.96 so the margin of error is 1.96* 0.06=0.118. Confidence interval is (.872-.848) +/- .118 which is (0.024 +/- .118)= (-0.094,0.142) Since the confidence interval includes 0 (no difference between the proportions) we would not reject (at the 95% level) the null hypothesis that the echinacea had no effect.

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