Echinacea is widely used as an herbal remedy for common cold, but does it work? Volunteers were randomly assigned to take either a placebo or an Echinacea supplement for 5 days following viral exposure. Among the 103 subjects taking Echinacea, 88 developed a cold, whereas 44 of 48 subjects taking a placebo developed a cold. (Make sure to check conditions) Construct a 97% confidence interval for the difference in the proportions of individuals developing a cold after viral exposure between the Echinacea and the placebo
Here, , n1 = 103 , n2 = 48
p1cap = 0.8544 , p2cap = 0.9167
Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.8544 * (1-0.8544)/103 + 0.9167*(1-0.9167)/48)
SE = 0.0529
For 0.97 CI, z-value = 2.17
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.8544 - 0.9167 - 2.17*0.0529, 0.8544 - 0.9167 +
2.17*0.0529)
CI = (-0.1771 , 0.0525)
Echinacea is widely used as an herbal remedy for common cold, but does it work? Volunteers...
Please use Rstudio to answer the following question. Thank you. In a double-blind experiment, healthy volunteers agreed to be exposed to a cold virus. They were either assigned to a control group (no echinacea but a placebo) or the group with echinacea. Here are the results Placebo group: 103 subjects 88 got a cold Echinacea group: 48 subjects 44 got a cold. a. Calculate the proportions getting cold in each group. b. Use a two-sample test to compare the proportions....