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Student Guide Book Subject: Statistics and Probability (ENG200801) Teaching Team: Ardiansyah Arian Dhini Arifin Djauhari Deni Ferdian Fia Fridayanti Adam Harinaldi Rini Prastyani Setiadi Tania Surya Utami Titin Siswantining Faculty of Engineering University of Indonesia 2011 This book is for non-co...

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Student Guide Book Subject: Statistics and Probability (ENG200801)

Teaching Team: Ardiansyah Arian Dhini Arifin Djauhari Deni Ferdian Fia Fridayanti Adam Harinaldi Rini Prastyani Setiadi Tania Surya Utami Titin Siswantining

Faculty of Engineering University of Indonesia 2011 This book is for non-commercial education purpose only. It contains figures, tables, chart, materials taken from various references.

Preface The knowledge of statistics and probability plays some important roles in many fields of engineering either in engineering research works or in the industrial application. In many situations, data processing and analysis heavily rely on the application of statistical methods in which their utilization will provide the basics for logical explanations about the relations that occur between variables of interest. As a subject of basic engineering science course to undergraduate program, Statistics and Probability will provide the basic knowledge and skills to the students to handle data and information appropriately starting from descriptive statistics to inferential statistics stages. This guidebook is intended to provide guidelines for students taking this subject. By reading this guidebook, it is expected that students understand the learning objectives and should be able to prepare themselves prior to each topic. It is also to guide students in working in group so that they may make the most of the group exercises. Any comments, critics, correction to this guidebook is thankfully accepted.

Depok, January 17th 2011 Teaching Team: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Ardiansyah Arian Dhini Arifin Djauhari Deni Ferdian Fia Fridayanti Adam Harinaldi Rini Prastyani Setiadi Tania Surya Utami Titin Siswantining

Table of Content Endorsement Page Preface Table of Content Chapter 1. General Information

1

Chapter 2. Learning Objectives

4

Chapter 3. Outlines of Subject

5

Chapter 4: Teaching Methods and Learning Activities

8

Chapter 5: Exercises and Assignments

11

Chapter 6. Assessment

14

References

16

Chapter

1

General Information 1. Subject

:

Statistics and Probability

2. Subject Code

:

ENG200801

3. Semester

:

3

4. Credit

:

3 SKS

5. Year

:

2010/2011

6. Type of Subject

:

Basic Engineering Subject (Mata Kuliah Dasar Teknik)

7. Prerequisite

:

None

8. Position of this subject in the curriculum structure of Bachelor of Engineering program

Fig. 1 Statistics and Probability position in the curriculum of Bachelor of Engineering program

Student Guide Book

Statistics and Probability – ENG200801

1

9. Teaching Team

: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Ardiansyah Arian Dhini Arifin Djauhari Fia Fridayanti Adam Harinaldi Rini Prastyani Setiadi Tania Surya Utami Titin Siswantining

10. Description of the subject Statistics and probability is a branch of applied mathematics which t is widely used in scientific method in collecting, classifying, summarizing, presenting, interpreting and analyzing data and information to support valid and reliable conclusions. Furthermore, the conclusions will be the basis for decision making process. The course of Statistics and Probability is intended to give a basic ability to a student to handle quantitative data and information starting with descriptive stage which includes collecting, organizing, and presenting the data in a scientific manner and then followed by inductive/inference stage which includes the process of estimating and drawing conclusion based on available data and relations between variables. Hence, the students are expected to be able to apply their knowledge of statistics in conducting experiments for their laboratory works/assignments as well as research works in their final projects. As a whole, the coverage of the Statistics and Probability course subject can be seen in Fig. 2 which describe the position of the topics within the procedures of a scientific method. Learning activities will be conducted through various method, which consists of: interactive lecture, question-based learning, discussion, demonstration and unguided structured assignments, case study, field assignment, etc. Assessment will be made continuously through a set of exercises, group discussion, mid semester exam and final exam. This guide book will help students prepare for learning activities throughout the semester for this subject. Preparation may include reading, preparation of worksheet and practice. Achievement of students will entirely be due to their activities and preparation. Construction of knowledge will be made through exercises, and questions available in this book. Students are expected to do the exercises, and they may move to further stage as they ready for that. Overall, students are expected to be active learners by acquiring knowledge through thinking and exercising. Students may also use this guidebook to self-assess their achievement.

Student Guide Book

Statistics and Probability – ENG200801

2

Introduction to Statistics and Data Analysis

start

problems Identification

Sampling collect available and relevant internal and external facts

N

is available facts sufficient?

collect new data from population/sample by using instruments, questionnaire, interview, etc.

Y classify, summarize, and process the data and calculate numerical descriptive measures

Descriptive Statistics

present and communicate summarized data in the form of tables, graphs, and include the numerical values of descriptive measures

Sampling Distribution

Probability Distribution

use the information from sample to:: 1. Estimate the value of parameter 2. Test the assumption/hypothesis of parameter

Y

information from sample ?

Probability concepts

N use the information from a census to evaluate the alternative steps and to make decisions

interpret the results, draw conclusions and make decisions.

Inference Techniques

- estimation - hypothesis test - regression and correlation

finish

Figure 2. Scope Statistics and Probability within the course of scientific method

Student Guide Book

Statistics and Probability – ENG200801

3

Chapter

2

Learning Objectives 2.1. Terminal Learning Objectives Upon completion of this subject students are expected to be able to handle quantitative data and information starting with descriptive stage which includes collecting, organizing, and presenting the data in a scientific manner and then followed by inductive/inference stage which includes the process of estimating and drawing conclusion based on available data and relations between variables. 2.2.

Supportive Learning Objectives

1. The students understand and can explain the role of statistics, its application in the engineering field and basic procedure of problem solving based on scientific methods. 2. The students are able to properly collect raw data, to organize them in a frequency distribution and eventually to present them in a histogram, polygon of frequency, bar graph, line graph, etc. 3. The students can calculate the descriptive measurement comprehensively including the central tendency, dispersion, skewness and kurtosis measurements and then summarize and describe the basic characteristics of data distribution. 4. The students are able to use the concepts of probability distribution, probability function/probability density function , cumulative distribution/function for discrete as well as continuous variable. 5. The students can apply some theoretical discrete distributions (Bernoulli, binomial, negative binomial, geometric, hyper geometric and Poisson) to solve some statistical problems related to engineering works 6. The students can apply some theoretical continuous distributions (Gaussian/norml, gamma, chisquare, exponential, Weibull, lognormal) to solve some statistical problems related to engineering works 7. The students can take proper steps to construct sampling distributions of the mean and proportion and can calculate the mean and standard deviations of those sampling distributions. 8. The students are able to conduct mean statistical estimation of the mean, proportion and variance of population based on data/information from sample. 9. The students can properly use hypothesis test procedures to draw conclusions in the problems involving one or two variables and also some advanced hypothesis test procedures (ANOVA, Chisquare test). 10. The students are able to calculate and to interpret the meaning of regression equation and error standard of estimations for simple linear regression analysis and then to use the measures obtained from regression and correlation analysis to make interval estimation of dependent variable for forecasting purposes.

Student Guide Book

Statistics and Probability – ENG200801

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Chapter

3

Outline of Subject Supportive Learning Objective

Topic

1, 2

1. Introduction to Statistics and Data Analysis

1.1 Overview : Statistical Inference, Samples, Populations 1.2 The role of Statistics and the Application in engineering 1.3 The role of computer in Statistics

[1] Chap.1 [2] Chap.1

1, 3

2. Descriptive Statistics

2.1. Discrete and Continuous Data 2.2. Sampling Procedures, Collection & Organization of Data 2.3. Graphical Methods and Data Description 2.4. Measure of Location : The sample Mean & Median Exercise 2.5. Measure of variability

[1] Chap. 1 [2] Chap. 2

1, 3, 4

3. Probability

3.1 Concept of Probability : sample space, events, counting sample points, probability of an event 3.2 Probability of an Event 3.3 Rules in Probability : additive, conditional, multiplicative, Bayes’ Rule

[1] Chap. 2 [2] Chap. 3

1, 3, 4

4. Random Variable

4.1 4.2 4.3 4.4

Concept of Random variable Discrete Probability Distribution Continuous Probability Distribution Probability Distribution with parameter 4.5 Mean of Random Variable 4.6 Variance of Random Variable

[1] Chap. 3 and Chap 4 [2] Chap. 4

1, 4, 5

5. Some of Discrete Probability Distribution

5.1 Discrete Uniform Distribution 5.2 Binomial and Multinomial Distribution 5.3 Hypergeometric Distribution

[1] Chap.5 [2] Chap.5

Student Guide Book

Sub-topic

Statistics and Probability – ENG200801

Reference

5

5.4 Negative Binomial & Geometric Distribution 5.5 Poisson Distribution

1, 4, 6

1, 7

6. Some of Continuous Probability Distribution

6.1 6.2 6.3 6.4 6.5 6.6

Continuous Uniform Distribution Normal Distribution Gamma & Exponential Distribution Chi Square Distribution Weibull Distribution Lognormal Distribution

[1] Chap.6 [2] Chap.6

7. Sampling Distribution

7.1 7.2 7.3 7.4 7.5

Definition and Basic Concept Sampling Distribution Sampling Distribution of Means Sampling distribution of Proporsion Sampling Distribution of Variance

[1] Chap.8 [2] Chap.7

8. Estimation

8.1 8.2 8.3 8.4

1, 9

9. One and Two-Sample Tests of Hypotheses

Inferential Statistics Classical Method of estimation Single Sample : Estimating the Mean Two Samples : Estimating the difference between Two Means 8.5 Single Sample : Estimating the Proportion 8.6 Two samples : Estimating difference between proportion 8.7 Single Sample : Estimating the Variance 8.8 Two Samples : Estimating the Ration between two variance 8.9 Sample Size Determination 9.1. Statistical Hypotheses : A General Concept 9.2. Testing a Statistical Hypotheses 9.3. One or Two-tailed Tests 9.4. P values for decision making in testing 9.5. One – or Two samples : Test of Means 9.6. One – or Two samples : Test of Proportion 9.7. One – or Two samples : Test of Variance 9.8. Chi square Test : Goodness of Fit, Independence, Homogenity, Several Proportion 9.9. ANOVA

1, 10

10. Simple Linear Regression

10.1. Introduction to Linear Regression 10.2. Simple Linear Regression model

1, 7, 8

Student Guide Book

Statistics and Probability – ENG200801

[1] Chap.9 [2] Chap.8

[1] Chap 9 and 10 [2] Chap.9, 10 and 11

[1] Chap 11 [2] Chap.12 6

1, 5, 6, 7, 10 11. Application of Statistics in Engineering

10.3. Inferences concerning regression coefficients 10.4. Simple Linear Correlation Analysis 11.1Statistics for Quality Control 11.2 Statistical Uncertainty 11.3 Time series analysis

[2] Chap. 14

Texbooks and Reference Books:

References : [1] Harinaldi, ”Prinsip-prinsip Statistik untuk Teknik dan Sains”, Erlangga, 2006. [2] Devore, J.L., Probability and Statistics for Engineering and The Sciences (5th Ed.), Duxbury, 2000 [3] Barnes J.W, Statistical Analysis for Engineers and Scientists, a Computer-Based Approach, McGrawHill, 1994 [4] Donald H.S, Statistics, A First Course (6th Ed), McGraw-Hill, 2001 [5] Walpole, Ronald E, Probability & Statistics For Engineers & Scientist, 8th Ed, Pearson Prentice Hall, 2007

Student Guide Book

Statistics and Probability – ENG200801

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Chapter

4

Teaching Methods and Learning Activities Week /Date

Week 1

Sub-topic

Supportive Learning Objective

1.1 Overview : Statistical Inference, Samples, Populations 1.2 The role of Statistics and the Application in engineering 1.3 The role of computer in Statistics

Week 2 2.1. Discrete and Continuous Data

Learning Methods Orient Exercise Feedbac ation (L) k (U) (O)

Media / Modul

1, 2

Interact ive Lecture

Individual Excercise, Self Study

Modul 1

1, 3

Interact ive Lecture

Group excersice, Self Study

Modul 2

1, 3, 4

Interact ive Lecture

Individual Excercise, Self Study

Modul 3

1, 3, 4

Interact ive Lecture

2.2. Sampling Procedures, Collection & Organization of Data 2.3. Graphical Methods and Data Description 2.4. Measure of Location : The sample Mean & Median Exercise 2.5. Measure of variability

Week 3 3.1 Concept of Probability : sample space, events, counting sample points, probability of an event 3.2 Probability of an Event 3.3 Rules in Probability : additive, conditional, multiplicative, Bayes’ Rule

Week 4 4.1 Concept of Random variable 4.2 Discrete Probability Distribution 4.3 Continuous Probability Student Guide Book

Statistics and Probability – ENG200801

Modul 4

8

Distribution 4.4 Probability Distribution with parameter 4.5 Mean of Random Variable 4.6 Variance of Random Variable

Week 5, 6

5.1 Discrete Uniform Distribution 5.2 Binomial and Multinomial Distribution 5.3 Hypergeometric Distribution 5.4 Negative Binomial & Geometric Distribution 5.5 Poisson Distribution

1, 4, 5

Interact ive Lecture

Individual Excercise, Self Study

Modul 5

Week 6, 7

6.1 Continuous Uniform Distribution 6.2 Normal Distribution 6.3 Gamma & Exponential Distribution 6.4 Chi Square Distribution 6.5 Weibull Distribution 6.6 Lognormal Distribution

1, 4, 6

Interact ive Lecture

Group excersice, Self Study

Modul 6

1, 7

Interact ive Lecture

Individual Excercise, Self Study

Modul 7

1, 7, 8

Interact ive Lecture

Individual Excercise, Self Study

Modul 8

1, 9

Interact ive Lecture

Group excersice, Self Study

Modul 9 and 10

Week 8 7.1 Definition and Basic Concept 7.2 Sampling Distribution 7.3 Sampling Distribution of Means 7.4 Sampling distribution of Proporsion 7.5 Sampling Distribution of Variance

Week 9 8.1 Inferential Statistics

Week 10, 11, 12

8.2 Classical Method of estimation 8.3 Single Sample : Estimating the Mean 8.4 Two Samples : Estimating the difference between Two Means 8.5 Single Sample : Estimating the Proportion 8.6 Two samples : Estimating difference between proportion 8.7 Single Sample : Estimating the Variance 8.8 Two Samples : Estimating the Ration between two variance 8.9 Sample Size Determination 9.1. Statistical Hypotheses : A General Concept 9.2. Testing a Statistical Hypotheses 9.3. One or Two-tailed Tests

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Statistics and Probability – ENG200801

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9.4. P values for decision making in testing 9.5. One – or Two samples : Test of Means 9.6. One – or Two samples : Test of Proportion 9.7. One – or Two samples : Test of Variance 9.8. Chi square Test : Goodness of Fit, Independence, Homogenity, Several Proportion 9.9. ANOVA

Week 13

Week 14

10.1. Introduction to Linear Regression 10.2. Simple Linear Regression model 10.3. Inferences concerning regression coefficients 10.4. Simple Linear Correlation Analysis 11.1 Statistics for Quality Control 11.2 Uncertainty of Statistics 11.3 Time Series Analysis

Student Guide Book

Individual Excercise, Self Study

Modul 11

1, 5, 6, 7, 10 Interact Individual

Modul 13

1, 10

Interact ive Lecture

ive Lecture

Statistics and Probability – ENG200801

Excercise, Self Study

10

Chapter

5

Exercises and Assignments Week /Date

Sub-topic

Assignment Group Assignment

Week 1

Assignment 1

1.1 Overview : Statistical Inference, Samples, Populations 1.2 The role of Statistics and the Application in engineering 1.3 The role of computer in Statistics

Week 2 2.1. Discrete and Continuous Data 2.2. Sampling Procedures, Collection & Organization of Data 2.3. Graphical Methods and Data Description 2.4. Measure of Location : The sample Mean & Median Exercise 2.5. Measure of variability

Individual Assignment

Data Collection, Data Description (Minitab) dan Measure of Location & variability

Week 3 3.1 Concept of Probability : sample

Assignment 2

space, events, counting sample points, probability of an event 3.2 Probability of an Event 3.3 Rules in Probability : additive, conditional, multiplicative, Bayes’ Rule

Week 4 4.1 Concept of Random variable

Assignment 3

4.2 Discrete Probability Distribution 4.3 Continuous Probability Distribution 4.4 Probability Distribution with Student Guide Book

Statistics and Probability – ENG200801

11

parameter 4.5 Mean of Random Variable 4.6 Variance of Random Variable

Week 5, 6

5.1 D...