Statistics and Probability Module 5 Test of Hypothesis

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General Mathematics – Grade 11 Alternative Delivery Mode Quarter 4 – Module 5: Test of Hypothesis First Edition, 2019 Republic Act 8293, section 176 states that: No copyright shall subsist in ... any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education – Region X – Northern Mindanao Regional Director: Dr. Arturo B. Bayocot, CESO III Development Team of the Module Author: Alfred G. Barrientos Mae Flor P. Cardeño Reviewers: Evangeline M. Pailmao Emily A. Tabamo Rufe A. Felicilda Management Team Chairperson: Dr. Arturo B. Bayocot, CESO III Regional Director Co-Chairperson: Dr. Victor G. De Gracia Jr. CESO V Asst. Regional Director Members Mala Epra B. Magnaong, Chief ES, CLMD Bienvenido U. Tagolimot, Jr., EPS-ADM Neil A. Improgo, EPS-LRMS Joel D. Potane, SEPS- LRMS Manager Himaya B. Sinatao, EPS-LRMS Printed in the Philippines by Department of Education – Bureau of Learning Resources (DepEd-BLR) Office Address: Zone 1, Upper Balulang Cagayan de Oro City 9000 Telefax: (088) 880-7071, (088) 880-7072 E-mail Address: [email protected] Development Team of the Module: Authors: Alfred G. Barrientos Mae Flor P. Cardeño Reviewers: Evangeline M. Pailmao Emily A. Tabamo Rufe A. Felicilda Illustrator: Jay Michael A. Calipusan Management Team: Chairperson: Dr. Arturo B. Bayocot, CESO III Regional Director Co-Chairpersons: Dr. Victor G. De Gracia Jr., CESO V Asst. Regional Director Mala Epra B. Magnaong CES, CLMD Members: Dr. Bienvenido U. Tagolimot, Jr. Regional ADM Coordinator Marino O. Dal EPS, Math Printed in the Philippines by: Department of Education – Regional Office 10 Office Address: Zone 1, Upper Balulang Cagayan de Oro City 9000 Telefax: (088) 880-7071, (088) 880-7072 E-mail Address: [email protected] 11 Statistics and Probability Module 5 Test of Hypothesis Department of Education • Republic of the Philippines This instructional material was collaboratively developed and reviewed by educators from public and private schools, colleges, and/or universities. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the Department of Education at [email protected]. We value your feedback and recommendations.v Table of Contents Overview ……………………………………..……..…… 1 Module Content ………………………………………………… 1 What I Need to Know ………………………………………………… 2 General Instructions ………………………………………………… 3 What I Know ………………………………………………… 4 Lessons/Concept Lesson 1 – Basic Concepts in Hypothesis Testing……………… 6 Activity 1 ………………………………………………… 6 Activity 2 …………….………………………………..… 7 Activity 3 ……………………………………………..…. 11 Activity 4 ………………………………………………… 15 Lesson 2 – Rejection Region and Level of Significance ……… 16 Activity 1 …………….………………………………… 21 Lesson 3 – Test on Population Mean…………………………….. 23 Activity 1 ………………………………………………… 23 Activity 2 ………………………………………………… 29 Lesson 4 – Test on Population Proportion .……………………… 30 Activity 1 ………………………………………………… 32 Activity 2 ………………………………………………… 35 Assessment ………………………………………………… 36 References ………………………………………………… 471 Module 5 Test of Hypothesis Overview Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. Basically, it is a process of gathering evidences to either accept or reject a claim, a guess, or an assumption, known as hypothesis. In real life, we are doing hypothesis testing every time we need to make decisions on something that affect our lives. As students you need to make decisions by looking both the positive and negative sides of the problem that confronted you before making any decision. Unknowingly, your decision to enroll in the Open Senior High School went to a series of hypothesis testing. You were confronted with a lot of “what ifs” until finally you decided to be here, one of the pioneers of the Open Senior High School Program. In the previous module, you learned that statistical inference is concerned with either estimation or evaluation of a statement or claim about a parameter or a distribution. The focus of this module is on evaluation of a claim about a parameter or a distribution which is done through a statistical test of hypothesis. This module will equip you with the basic knowledge in testing hypothesis concerning population mean and population proportion which in turn will prepare you to your future journey to the world of practical research. The lessons are arranged and presented in an easier way and are supplemented with activities and exercises that would concretize your learning. So, sit back, relax and enjoy doing the module. Module Contents The lessons that we will be dealing with are the following:  Lesson 1 – Basic Concepts in Hypothesis Testing  Lesson 2 – Rejection Region and Level of Significance  Lesson 3 – Test on Population Mean  Lesson 4 – Test on Population Proportion2 What I need to know? Once you are done with this module, you should be able to: 1. illustrate (a) null hypothesis, (b) alternative hypothesis, (c) level of significance, (d) rejection region, and (e) types of errors in hypothesis testing (M11/12SP-IVa-1). 2. calculates the probabilities of committing a Type I and Type II error (M11/12SPIVa-2). 3. identifies the parameter to be tested given a real-life problem (M11/12SP-IVa-3) 4. formulate the appropriate null and alternative hypothesis on a population mean (M11/12SP-IVb-1) 5. identify the appropriate form of the test-statistic when: (a) the population variance is assumed to be known (b) the population variance is assumed to be unknown; and (c) the Central Limit Theorem is to be used (M11/12SP-IVb-2) 6. identify the appropriate rejection region for a given level of significance when: (a) the population variance is assumed to be known (b) the population variance is assumed to be unknown (c) the Central Limit Theorem is to be used (M11/12SP-IVc-1) 7. compute for the test-statistic value of population mean (M11/12SP-IVd-1). 8. draw conclusion about the population mean based on the test-statistic value and the rejection region (M11/12SP-IVd-2). 9. solve problems involving test of hypothesis on the population mean (M11/12SPIVe-1). 10.formulate appropriate null and alternative hypotheses on a population proportion (M11/12SP-IVe-2), 11.identify the appropriate form of test statistic when the Central Limit Theorem is to be used (M11/12SP-IVe-3), 12.identify the appropriate rejection region for a given level of significance when the Central Limit Theorem is to be used (M11/12SP-IVe-4), 13.compute for the test statistic value of population proportion (M11/12SP-IVf-1), 14.draw conclusion about the population proportion based on the test-statistic value and the rejection region (M11/12SP-IVf-2), and 15. Solve problems involving test of hypothesis on the population proportion (M11/12SP-IVf-2) [Show More]

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