5. Some states that operate a lottery believe that restricting the use of lottery profits to supporting education makes the lottery more profitable. Other states permit general use of the lottery income. The profitability of the lottery for a group of states in each category is given below: State Lottery Profits For Education For General Use % Profit State State % Profit New Mexico 24 Massachusetts 21 Idaho 25 Maine 22 Kentucky 28 lowa 24 South Carolina 28 Colorado 27 Georgia 28 Indiana 27 Missouri 29 District of Columbia 28 Ohio 29 Connecticut 29 Tennessee 31 Pennsylvania 32 Florida 31 Maryland 32 California 35 North Carolina 35 New Jersey 35 # of States 12 of States Mean 29.833 Mean 26.889 SL. Dev 3.7132 St Dev. 3.9511 Let ui denote the mean profitability of states who use their lottery profits for education, and u2 denote the mean profitability of states who use their lottery profits for general use. (a) State the appropriate hypotheses to be tested for this problem (refer to the motivation behind this problem stated before the table). (b) Draw a picture of the rejection region on the appropriate curve, and identify the critical value. Assume that a significance level of a = 0.1 is to be used. (c) Calculate the value of the appropriate test statistic; make sure to show all of your intermediate work to ensure the potential of obtaining partial credit. (d) What should be the decision and conclusions of this hypothesis test?
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 C and D
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