1. The average score of students in statistics class is 81 out of 100. This year the average score of around 200 students is 83 with a standard deviation of 10. Is this unusual? a. Construct the null hypothesis b. Construct the alternative hypothesis c. Is this a two-tailed or one-tailed t-test? Why?
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.
Choose the letter of the correct answer.
![Learning Tasks/Activities 2.1
Look for a newspaper, news magazines, and some Internet articles. Find articles from which
you can write a null and alternate hypothesis.
Assessment 2.1
Instruction: Read each item carefully and choose the letter of the correct answer.
1. The average score of students in statistics class is 81 out of 100. This year the average
score of around 200 students is 83 with a standard deviation of 10. Is this unusual?
a. Construct the null hypothesis
b. Construct the alternative hypothesis
c. Is this a two-tailed or one-tailed t-test? Why?
2. For example, before the pandemic, students from the 7:00 am class reported that they
sleep on average 6 hours. However, the report shows that it is uncertain whether students
longer than six hours or less than 6 hours. Someone consulted you on how to provide
statistical evidence whether the students sleep less 6 hours or more than 6 hours.
a. Construct the null hypothesis
b. Construct the alternative hypothesis
c. Is this a two-tailed or one-tailed t-test? Why?
d. Discuss in detail what you will do to address this problem.
e. How about you? How long do you sleep daily?
3. State the null and alternative hypotheses (in symbols and in words) for each of the
following situations.
a. The average time workers spent commuting to work five years ago was 38.2
minutes. It was believed that the average figure is less now.
b. The mean salary for all men in a certain profession is 25 000 pesos. A special
interest group thinks that the mean salary for women in the same profession is
different.
c. The recognized figure for the caffeine content of an 8-ounce cup of coffee is 133
mg. A dietitian believes that the average for coffee served in a local restaurant is
higher.
d. The average yield per acre for all types of corn in a recent year was 161.9 bushels.
An economist believes that the average yield per acre is different this year.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ac29330-f582-4e33-a79a-a2bf31f2134f%2F5e49d4e0-151a-4750-bb37-6a36bda56d74%2F62fhe2i_processed.jpeg&w=3840&q=75)
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