Probabilistic System Analysis Lecture by Dr. Erwin Sitompul at President University
In this lecture series, Dr. Erwin Sitompul discusses probabilistic system analysis, focusing on estimating proportions and variances in single samples. The content includes insightful discussions, practical examples, and informative images to aid in understanding the concepts presented. Follow along as Dr. Sitompul delves into the intricacies of statistical analysis, providing valuable insights for students, researchers, and professionals alike.
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Presentation Transcript
Probabilistic System Analysis Lecture 13 Dr.-Ing. Erwin Sitompul President University http://zitompul.wordpress.com 2 0 2 1 President University Erwin Sitompul PSA 13/1
Chapter 9.10 Single Sample: Estimating a Proportion Estimating a Proportion President University Erwin Sitompul PSA 13/2
Chapter 9.10 Single Sample: Estimating a Proportion Estimating a Proportion President University Erwin Sitompul PSA 13/3
Chapter 9.10 Single Sample: Estimating a Proportion Estimating a Proportion President University Erwin Sitompul PSA 13/4
Chapter 9.10 Single Sample: Estimating a Proportion Estimating a Proportion There will be difference between p and its estimate . But we can be sure that the difference will be within President University Erwin Sitompul PSA 13/5
Chapter 9.10 Single Sample: Estimating a Proportion Estimating a Proportion President University Erwin Sitompul PSA 13/6
Chapter 9.12 Single Sample: Estimating the Variance Estimating the Variance Theorem 8.4 If S2 is the variance of a random sample of size n taken from a normal population having the variance 2, then the statistic ( 2 2 2 1 i = ) 2 X X 2 ( 1) n n S = i = has a chi-squared distribution with v=n 1 degrees of freedom. President University Erwin Sitompul PSA 13/7
Chapter 9.12 Single Sample: Estimating the Variance Estimating the Variance President University Erwin Sitompul PSA 13/8
Chapter 9.12 Single Sample: Estimating the Variance Estimating the Variance President University Erwin Sitompul PSA 13/9
Chapter 9.12 Single Sample: Estimating the Variance Estimating the Variance President University Erwin Sitompul PSA 13/10
Chapter 9.12 Single Sample: Estimating the Variance Estimating the Variance President University Erwin Sitompul PSA 13/11
Probabilistic System Analysis Homework 13A 1.An english course organizer claims that 89% of the enrolled participants are satisfied with the teachers performance. Some in a group of 119 participants question the claim, where 99 of them confirm that they are indeed satisfied with the teachers performance. a. Find the 95% confidence interval for the actual proportion of satisfied participants. b. Assuming that the claim of the organizer is correct, find the probability that only 99 out of 119 participants are satisfied with the teachers performance. 2.Determine how many respondents must at least be asked so that the result of an election can be predicted within 2.5% margin of error with 95% confidence level. President University Erwin Sitompul PSA 11/12
