The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a = 0.10, can you reject the dean's this claim. claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.9 8.6 13.8 6.1 5.2 9.3 13.4 8.20 (a) Write the claim mathematically and identify Ho and Ha- Which of the following correctly states Ho and H,? OA. Ho: Hs11.0 O B. Ho: H=11.0 OC. Ho: >11.0 H: u>11.0 Hai u#11.0 Hgi us11.0 OD. Ho: H#11.0 O E. Ho:H<11.0 OF. Ho: H211.0 H,: u=11.0 Hai H211.0 Hiu<11.0 (b) Use technology to find the P-value. P= (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? O A. Fail to reject Ho because the P-value is greater than the significance level. O B. Reject Ho because the P-value is less than the significance level. O C. Reject Ho because the P-value is greater than the significance level. O D. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A. At the 10% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is greater than 11.0. OC. At the 10% level of significance, there is sufficient evidence to reject the O B. At the 10% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is less than 11.0. claim that the mean number of classroom hours per week for full-time faculty is 11.0. O D. At the 10% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is 11.0.
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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