[MMW] Part 3: Inferential Statistics & Problem-solving

Hypothesis

It is an assumption or an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world.

A. Null Hypothesis (𝐻𝑜)

B. Alternative Hypothesis (𝐻𝑎)

two kinds of hypotheses:

Null Hypothesis (𝐻𝑜)

is the hypothesis that must always express the idea of non-significance of difference, lack of association or relationship between variables. The rejection of this hypothesis implies the acceptance of the alternative hypothesis.

Alternative Hypothesis (𝐻𝑎)

It specifies the existence of a difference (or that one group is better than the other), association or relationship between the dependent and independent variables. The acceptance of the null hypothesis implies the rejection of this hypothesis.

𝑯𝒐: Online gaming has no significant effects on the

academic achievements of high school freshman

students. (non-directional hypothesis/two-tailed test)

𝑯𝒂: Online gaming has negative effects on the

academic achievements of HS freshman students

(directional hypothesis/one-tailed test)

(Under Hypothesis) Title: The Effects of Online Gaming on the Academic

Achievements of Freshman High School Students

𝑯𝒐: There is no significant correlation between

competencies in English and Mathematics.

𝑯𝒂: There is a significant correlation between

competencies in English and Mathematics.

(Under Hypothesis) Correlation between Competencies in English and Mathematics

Type I error

(alpha error or false positive) – rejecting a true null hypothesis

Type II error

(beta error or false negative) – accepting a false null hypothesis

Problem

a task that requires the learner to reason through a situation that will be challenging but not impossible

Exercise

provides practice in using algorithms and maintaining the basic facts.

Problem Solving

encompasses exploring, reasoning, strategizing, estimating, conjecturing, testing, explaining, and proving.

Exercise/Drill

is a set of number sentences intended for practice in the development of a skill

George Polya.

The most famous study of problem-solving techniques was developed by him, He is known to be “The Father of Problem-Solving”.

1. Understand the problem (find it out) – Read the problem, if possible, several times, and analyze it carefully.

2. Devise a plan (think) – Devise what appropriate strategy to attack a problem.

3. Carry out the plan (solve it) – After knowing a strategy, carry out your plan of attack.

4. Look back (verification) – Check if your answer is reasonable.

Steps in Problem-Solving: (4)

Deductive Reasoning

(Approaches to Problem Solving) one arrives at a specific conclusion based on general assumptions, procedures, or principles.

Deductive Reasoning

(Approaches to Problem Solving) It is the process of reasoning to a specific conclusion from general statement.

Examples: A quadrilateral has four sides. A square has four sides. Therefore, a square is a quadrilateral.

Inductive Reasoning

(Approaches to Problem Solving) one makes generalizations based on individual instances or specific observations.

Inductive Reasoning

(Approaches to Problem Solving) Often used by mathematicians and scientists to predict answers to complicated problems.

Examples:

1 + 3 = 4

5 + 7 = 12

11 + 13 = 24

Therefore, the sum of any two odd numbers is an even number.

Routine Problem

Using at least one of the four arithmetic operations and/or ratio to solve problems.

Example: A sales promotion in a store advertises a jacket regularly priced at Php1255.98 but now selling for 20% off the regular price. The store also waives the tax. You have Php1000 in your pocket. Do you have enough money to buy the jacket?

Non-routine Problem

May be solved in many different ways or strategies and may have more than one answer or solution.

Ex: Mrs. Rivera wishes to tile her classroom floor with square tiles. She wants to use whole tiles, without cutting any pieces. The rectangular floor has dimensions 8.4 meters by 7.2 meters. What is the minimum number of whole identical