Question: Problem 11.44

Volunteers who had developed a cold within the previous 24 hours were randomized to take wither a zinc lozenge or placebo lozenge every 2 to 3 hours until their cold symptoms were gone. 25 participants took zinc lozenges and 23 participants took placebo lozenges. 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 \({{\bar{X}}_{1}}\), \({{\bar{X}}_{1}}-{{\bar{X}}_{2}}\) = difference in sample means and also compute the unpooled \(se\left( {{{\bar{X}}}_{1}}-{{{\bar{X}}}_{2}} \right)\) = standard error of the difference in means.

a.) 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 unpooled standard error and use the smaller

of 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.