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Unformatted text preview: Chapter 18 Sampling Distribution Models ActivStats: 18 Read: Chapter 18 1. Sampling Distribution of Proportion Suppose that p is an unknown proportion of elements of a certain type S in a population For example 1. Proportion of left-handed people in Michigan 2. Proportion of students at MSU who carry cell phones with them 3. Proportion of voters who will vote for Mr. X in the next election In order to estimate p we select a random sample of size n from the population, compute the number x of elements of type S in the sample and compute the sample proportion n x p = ˆ p ˆ is our estimate of p. Example : Suppose that we want to estimate the proportion p of students in a certain college who carry cell phones with them, and that 187 out of randomly selected 285 students of the college indicated that they had cell phones with them. Then n = 285, x = 187, and % 6 . 65 656 . 285 187 ˆ = = = p is our estimate of p, hence approximately 65.6% of students in this college carry cell phones with them. . QUESTION. What is an error | ˆ | p p- of estimation? (Can we answer this without knowledge of real value of p? ) p APPROACH. Suppose that we take another sample of 285 students and compute p ˆ (clearly will be different than 0.656), and then again, and again... 0....
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This note was uploaded on 07/25/2008 for the course STT 200 taught by Professor Dikong during the Summer '08 term at Michigan State University.
- Summer '08