3) Handedness and Occupation Is the career someone chooses associated with being left- or right-handed? In one study a sample of Americans from a variety of professions were asked if they consider themselves left- handed, right handed, or ambidextrous (equally skilled with the left and right hand). The results for five professions are shown in this table. Test for an association between handedness and career for these five professions. State the null and alternative hypotheses, calculate the test statistic (i.e. x²), find the p-value, and write a conclusion. Left Total Right 101 115 Ambidextrous 118 Psychiatrist Architect Orthopedic Surgeon Lawyer Dentist Total 10 26 148 121 5 6 132 83 16 6. 105 116 10 132 536 67 32 635 4) Clinical Trial of Lipitor Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. Adverse reactions have been studied in clinical trials, and the table below summarizes the results for infections in patients from different treatment groups. Use a 0.05 significance level to test the claim that there is an association between infections and treatment. Does atorvastatin treatment appear to have an effect on infections? Placebo Atorvastatin 10mg Atorvastatin 40mg Atorvastatin 80mg Infection 27 89 8. 7 No Infection 243 774 71 87
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.
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