In a study designed to test the effectiveness of echinacea for treating upper respiratory tract infections in children, 337 children were treated with echinacea and 370 other children were given a placebo. The numbers of days of peak severity of symptoms for the echinacea treatment group had a mean of 6.0 days and a standard deviation of 2.3 days. The numbers of days of peak severity of symptoms for the placebo group had a mean of 6.1 days and a standard deviation of 2.4 days (based on data from “Efficacy and Safety of Echinacea in Treating Upper Respiratory Tract Infections in Children,” by Taylor et al., Journal of the American Medical Association, Vol. 290, No. 21).

a. Construct the 95% confidence interval for the mean number of days of peak severity of symptoms for those who receive echinacea treatment.

b. Construct the 95% confidence interval for the mean number of days of peak severity of symptoms for those who are given a placebo.

c. Compare the two confidence intervals. What do the results suggest about the effectiveness of echinacea?