4. You are running a pharmaceutical drug trial. You divide the 100 people in the study into two groups: one group receives the drug, while the other receives a placebo. Then you assess their health to determine whose health has improved. The results are cross- tabulated below: Improved No Change 45 Drug Placebo 50 40 15 (a) What is the proportion of people whose health did not change, given they took the placebo? 15+40= 55 (b) What is the proportion of people whose health did not change, given they took the drug? 44 50= 95 bi 0 G5 O.52 11 (c) What is the proportion of people whose health has improved among all people in the trial? What is this type of proportion called? 45t 15t50 +40 150 Manginal paparton 45t15-00 0.4 150 8800 (d) Draw a stacked bar graph using your proportions from (b) and (c) and the fact that someone's health can only improve or not improve (there are only two possibilities). endo qo (e) Do you think the drug is more effective than the placebo? Why or why not? 4
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Part D.
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