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 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 1.3 days. for the placebo group, the mean overall duration of symptoms was 7.7 days, and the standard deviation was 2 days. assume that the duration of symptoms in each group is normally distributed.
a) what is the width of the 95% confidence interval for estimating the difference between the mean duration of symptoms in the two groups?
b) further assume that the standard deviation of the duration of symptoms in the zinc lozenge group equals that in the placebo lozenge group.
what is the width of the 95% confidence interval for estimating the difference between the mean duration of symptoms in the two groups?
c) further assume that the standard deviation of the duration of symptoms in the zinc lozenge group equals that in the placebo lozenge group.
we want to investigate if the mean overall duration of symptoms in the placebo group exceeds the mean overall duration in the zinc lozenge group by at least 2 days. what is the value of the appropriate test statistic for checking that?
d) further assume that the standard deviation of the duration of symptoms in the zinc lozenge group equals that in the placebo lozenge group.
we want to investigate if the mean overall duration of symptoms in the placebo group exceeds the mean overall duration in the zinc lozenge group by at least 2 days. what is the p-value of the appropriate test for checking that?