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Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Unformatted text preview: Stat 312: Lecture 7 Confidence Intervals III. Moo K. Chung mchung@stat.wisc.edu February 11, 2003 Concepts 1. If n is sufficiently large, approximate 100(1 - )% confidence interval for is x z/2 s/ n, where s is the sample stan dard deviation. 2. Let p denote the proportion of an individual with a specified property. 100(1 - )% CI for a population proportion p is ^^ p z/2 pq /n. ^ [33] 1 1 0 0 0 0 1 0 1 0 0 [49] 0 1 0 0 0 0 1 1 0 1 0 [65] 0 0 1 0 0 1 0 0 0 1 0 [81] 1 0 1 0 0 1 1 0 0 0 1 [97] 0 1 1 0 > sd(X) [1] 0.4878317 > 0.38+1.96*0.49/sqrt(100) [1] 0.47604 > 0.38-1.96*0.49/sqrt(100) [1] 0.28396 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 Exercise 7.23. Use Concept 2. 3. One-sided confidence interval: An upper When 37 helmets were subjected to a certain imconfidence bound for is pact test, 24 showed damage. Let p denote the proportion of helmets that would show damage < x + z s/ n under the test. Find a 99% CI for p. and a lower confidence bound for is > x - z s/ n. Self-study problems Example 7.8., 7.8. Use Concept 2. In-class problems Ex. Toss n = 100 biased coins with P (H) = p. Suppose you observe 38 heads. Construct 95% CI of p. rbinom(n,1,p) will generate a Bernoulli random sample of size n with P (Xi = 1) = p. > X<-rbinom(100,1,0.4) > X [1] 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 [17] 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 ...
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Spring '04 term at Wisconsin.

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