Can music help you study? It has been claimed that listening to music while studying enhances concentration and consequently helps an individual to absorb more information. To figure this out, your former high school teacher decided to implement it on a random sample of students. Each randomly selected student was assigned to study in a classroom under a certain environment (Classrooms A, B, and C). Classroom A had constant music being played in the background, classroom B had variable music being played, and classroom C was a regular class with no music playing. After a month, a test was conducted for all three groups and their test scores were collected. Aside from determining the test scores of the students, the teacher also asked the students to personally rate their level of concentration which is measured from 1 to 5, with codes 1 as very low concentration, 2 as low concentration, 3 as moderate concentration, 4 as high concentration, and 5 as very high concentration. 1. Your former high school teacher wants to study if the mean test scores differ among the three environments (A, B, and C). She then asked your statistical advice considering that you have enough knowledge that using a parametric test specifically the F-test in Analysis of Variance (ANOVA) can answer her objective. Consider the graphs and results for the test of the assumptions that were generated using the R Commander (see page 2). a. Discuss and interpret the results obtained in both the graphs and statistical tests b. What will you recommend to your high school teacher? Will you recommend a parametric test or a non- parametric test? Briefly explain your answer.
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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