one year of completing their undergraduate degree. Suppose we conduct a survey and find out that 350 of the 448 randomly sampled graduates found jobs. The graduating class under consideration included 4950 students. For each of the following use appropriate computational software and be sure that your answer has at least 4 decimal digits of accuracy. (a) What is the value of the point estimate for the proportion of graduates who found a job within one year. (b) We need to check if the conditions for constructing a confidence interval based on these data are met. Recall that the conditions are that we expect at least 10 successes, at least 10 failures, and we are sampling independent individuals. To check the last one we need to make sure that we are gathering no more than about 10% of the total population. This is especially important since the survey is done without replacement. How many successes do we expect? np = > 10 How many failures do we expect? n(1 – p) > 10 %3D Based on the 10% rule stated above, can we assume that the individuals are independent? ? (c) Calculate a 95% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this university. (round your critical z-score to two decimal places) Lower Bound:p – z* × SE = Upper Bound: p+ z* × SE =
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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