Question: Volunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty five participants took zinc and 23 took placebo lozenges. The mean overall duration of symptoms for the zinc group was 4.5 days, and the standard deviation of overall duration of symptoms was 1.6 days. For the placebo group, the mean overall duration of symptoms was 8.1 days, and the standard deviation was 1.8 days.

Refer to above about the effect of zinc lozenges on the duration of cold symptoms. For n = 25 in the zinc lozenge group, the mean overall duration of symptoms was 4.5 days, and the standard deviation was 1.6 days. For n = 23 in the placebo group, the mean overall duration of symptoms was 8.1 days and the standard deviation was 1.8 days.

a. Calculate x₁ - x₂ = difference in sample means and also compute the unspooled s.e. (x₁ - x₂) = standard error of the difference in means.

b. Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments, and write a sentence interpreting the interval. Use the unspooled standard error and use the smaller of the n₁ – 1 and n₂ – 1 as a conservative estimate of degrees of freedom.

c. Is the interval computed in part (b) evidence that the population means are different? Explain.