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.,...

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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 in a
population of individuals like those who used the zinc lozenges.
b. Calculate a 95% confidence interval for the mean overall duration of symptoms in a
population of individuals like those who used the placebo lozenges.
c. On the basis of the intervals computed in parts (a) and (b), is it reasonable to conclude
generally that taking zinc lozenges reduces the overall duration of cold symptoms? Explain why
you think this is or is not an appropriate conclusion.
d. 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)?
Solution:
Data
Zinc lozenges Placebo lozenges
Mean 4.5 8.1
SD 1.6 1.8
N 25 23
Confidence interval gives an estimated range of values for any given parameter. This range is
calculated from the given sample data.
In order to calculate the 95% confidence interval for the mean overall duration of symptoms, we
need to use the appropriate formula from the following.
Upper and Lower Limit at 95% for sample > 30 = M ± (Z1-α/2 * SD/√N)
Upper and Lower Limit at 95% for sample < 30 = M ± (t1-α/2 N-1 * SD/√N)
As N = 25 which is < 30, we have to use the following formula.
Upper and Lower Limit at 95% for Population Mean = Sample M ±...