Twenty-five volunteers who had developed cold symptoms within the last 24 hours were given zinc lozenges to take every 2 to 3 hours until their cold symptoms were gone. The mean overall duration of symptoms was 4.5 days with a standard deviation of 1.6 days. The selected cases have a distribution which appears to be symmetric and bell-shaped.
a. Construct a 99% confidence interval for the mean overall duration of symptoms in a population of individuals who used zinc lozenges.
b. In a previous test, the mean overall duration of symptoms for volunteers who were told to drink an herbal tea for relief of their symptoms was 7 days. Based on your confidence interval, do you think that using the lozenges reduces the overall duration of symptoms compared to using the herbal tea?