Question

a generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). in a randomized, double-blind experiment with 200 patients, 100 are given the name - brand drug (control group) and 100 are given a generic version of the drug (treatment group). in the control group, the average reduction in blood pressure is 15.2 mmhg with a standard deviation of 11.5 mmhg. in the treatment group, there is an average reduction of 14.6 mmhg and a standard deviation of 12.5 mmhg. neither group has any outliers. a researcher claims that this study shows the generic drug is not as effective as the name - brand drug. what would be the reply of a statistician?

you have two attempts for this problem so choose wisely. if you do not receive 5 points in the gradebook after submitting this assignment then you have answered incorrectly. make sure to try it again before the deadline.

○ the point estimate for the generic drug is lower than that of the name - brand drug, which means the generic drug is less effective. the researcher is correct.

○ the standard deviations are quite large within each group relative to the size of the difference in point estimates. it is unclear if there is a real difference in the effectiveness of the two drugs or if the difference is just due to chance.

○ while there is some uncertainty in the point estimates, the sample sizes for each group are large, indicating that the difference must be real.

○ because the difference in sample means is under 1 mmhg, we can safely conclude the drugs are equally effective.

question help: message instructor post to forum

Explanation:

Step1: Analyze the standard deviation

The standard deviations \(15.2\) and \(12.5\) are large relative to the difference in means (\(15.5 - 14.6=0.9\)). A large standard deviation means there is a lot of variability within each group.

Step2: Consider the significance of the difference

Just because the point - estimate of the mean of the treatment group (\(14.6\)) is less than that of the control group (\(15.5\)) does not mean there is a real difference. With large standard deviations, the observed difference could be due to random chance.

Answer:

The standard deviations are quite large within each group relative to the size of the difference in point estimates. It is unclear if there is a real difference in the effectiveness of the two drugs or if the difference is just due to chance.