An experiment is to be designed to compare two drugs, Drug A and Drug B$,$ both designed to reduce blood presure. Drug A is a new formulation. Drug B is a formulation that has been used for some years$)$ You have been provided with $40$ volunteers, all of whom suffer from high blood pressure. Twenty of the volunteers will receive Drug A$,$ and the other twenty will receive Drug B$.$ The reduction in blood pressure will be measured for each participant.

$($a$)$ Explain how the $40$ volunteers might be randomly assigned to the two groups.

$($b$)$ Why would the volunteers be assigned randomly to the two groups, rather than, for example, allowing each volunteer $($independently of the other volunteers$)$ to choose which group he$/$she would be in$?$

$($c$)$ Suppose the blood pressures of the volunteers who are given Drug A are reduced significantly more, on average, than the blood pressures of the volunteers who are given Drug B$.$ Explain why we have evidence that Drug A causes a greater reduction in blood pressure than Drug B$.$

$($i$)$What two criteria are required for the experiment to be described as double$-$blind"?

$($ii$)$Explain why the two criteria you provided above are important in this experiment.

$($iii$)$What would need to be the case for the experiment to be described as "single$-$blind"?

$($e$)$ Suppose an experiment were to be designed to determine the effect of regular exercise on people's blood pressure. Explain why a double$-$blind design is not possible for this experiment.