Listed below are the numbers of words spokan in a day by each member of eight difforant randomly selectad couples. Complote parts (a) and (b) belour 15.394 25.400 1424 7724 19.124 16.089 13.706 24.823 D Male Female 24.950 13.913 18.529 18.241 12.726 16.505 16.518 18.624 a. Use a 0.01 significance level to test the claim that among couples, males speak fewer words in a day than females In this example, g is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the oords spoken by the male minus words spoken by the female What are the null and alternative hypotheses for the hypothesis test? HgH 0 wordis) H, < O wordis) (Type integers or decimals Do not round) Identify the test statistic t= -0.59 (Round to two decimal places as needed) Identify the P-value Pvalue = 0.288 (Round to three decimal places as needed) What is the conclusion based en the hypothesis test? Since the Pvalue is greater than the significance level, fall to reject the null hypothesis. There is not sufficient evidence to support the claim that males speak fever words in a day than females b. Construct the cenfidance interval that could be used for the hypethesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The cenfidence interval iswordis) < wordis) (Round to the nearest integer as needed)
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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