Statistics Probability Q3 Mod8 Length of Confidence Interval PDF

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Statistics and ProbabilityQuarter 3 – Module 8:Length of Confidence Interval andAppropriate Sample Size`Statistics and Probability Alternative Delivery Mode Quarter 3 – Module 8: Length of Confidence Interval and Appropriate Sample SizeFirst Edition, 2020Republic Act 8293, section 176 states that: N...

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Statistics and Probability Quarter 3 – Module 8: Length of Confidence Interval and Appropriate Sample Size `

Statistics and Probability Alternative Delivery Mode Quarter 3 – Module 8: Length of Confidence Interval and Appropriate Sample Size First Edition, 2020 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, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module 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 Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

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Statistics and Probability Quarter 3 – Module 8: Length of Confidence Interval and Appropriate Sample Size

Introductory Message This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson. Each SLM is composed of different parts. Each part shall guide you step-bystep as you discover and understand the lesson prepared for you. Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these. In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning. Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task. If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Thank you.

What I Need to Know

At the end of the lesson, the learner should be able to: ➢ Identify the length of a confidence interval. (M11/12SP-IIIj-1) ➢ Compute for the length of the confidence interval. (M11/12SP-IIIj-2) ➢ Compute for an appropriate sample size using the length of interval. (M11/12SP-IIIj-3) ➢ Solve exercise involving sample size determination. (M11/12SP-IIIj-4) .

What I Know

A. Find the length of the following confidence interval. 1. 0.0254 < p < 0.560 2. 0.385< p < 0.655 3. 0.363 < p < 0.655 4. Upper confidence limit = 0.632 Lower confidence limit = 0.475 5. Upper confidence limit = 0.686 Lower confidence limit = 0.415

B. Find the length of the confidence interval given the following data: 6. 𝑠 = 8.47, n = 300, confidence level= 95%

7. 𝑠 = 6.25, n = 150, confidence level= 95%

8. 𝑠 = 4.36, n = 350, confidence level= 99%

9. s = 5.25, n = 16, confidence interval = 95% 10. s = 7.15, n = 20, confidence interval= 99%

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Lesson

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Length of Confidence and Appropriate Sample Size

How large should be the sample? Many researchers find this a problem. In fact, many rely on old methods to determine the sample size they need in their investigations. This problem must be addressed carefully because needlessly large samples are a waste of important resources. On the other hand, insufficient sample size may lead to poor results.

What’s In

A. Fill in the blank with the correct word or group of words to make a meaningful statement. Write your answer on a separate sheet of paper. 1. Statistically, rounding up of 111.12 is____________________. 2. A confidence level is the confidence coefficient and is expressed as __________________. 3. For a 95% confidence level, the confidence coefficient is __________________. 4. When a 99% confidence level is selected, a = _______________. 5. The standard deviation of a sampling distribution is called _____________. 6. A subset of the interest population is called ______________. B. Answer the following: 1. 1 – 0.38 2. (0.35) (0.65) 3.

1.96(2) 0.06

4. (

5. (

(1.96)(5.3) 2 ) 0.2

(2.58)(2.5) 2 0.10

)

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Note to the Teacher In this module, the learners will be able to know how to compute for the length of the confidence interval and for an appropriate sample size needed using the length of interval.

What’s New

Definition of Terms 1. Confidence interval - In statistics, this refers to the probability that a Population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. 2. Narrowness of the interval – This pertains to a small width in relation to the length of the confidence interval.

Length of Confidence Interval This refers to the absolute difference between the upper confidence limit and the lower confidence limit.

Formula: LCI = |UCL – LCL|

= |LCL – UCL|

Or LCI = UCL – LCL Where: LCI – length of confidence interval UCL – upper confidence limit LCL – lower confidence limit

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Example 1. Find the length of the confidence interval 0. 275...