Consider an experiment in which a subject performs a task while being exposed to two different stiumli (for example, sound and light). For low levels of the stimuli, the subject's performance might actually improve, but as the stimuli increase, they eventually become a distraction and the performance begins to deteriorate. Suppose in a certain experiment in which x unites of stimulus A and y unites of stimulus B are applied, the performance of a subject is measured by the funtion f(x,y) = C+xye(1-x^2-y^2) where C is a positive constant. How many units of each stimulus result in maximum performance?

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.