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 (prasad et al., 2000). twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. the mean overall duration of symptoms for the zinc lozenge 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. a. calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the zinc lozenges. b. calculate a 95% confidence interval for the mean overall duration of symptoms if everyone in the population were to take the placebo lozenges. c. draw a picture similar to figure 11.7 on page 426 illus-trating the confidence intervals you found in parts (a) and (b).d. on the basis of the intervals computed in parts (a) and (b) and/or the picture you constructed in part (c), is it reasonable to conclude generally that taking zinc loz-enges reduces the overall duration of cold symptoms more than if taking a placebo? explain why you think this is or is not an appropriate conclusion. e. in their paper, the researchers say that they checked whether it was reasonable to assume that the data were sampled from a normal curve population and decided that it was. how is this relevant to the calculations done in parts (a) and (b)?