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

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Stat 312: Lecture 7 Confidence Intervals III. Moo K. Chung [email protected] February 11, 2003 Concepts 1. If n is sufficiently large, approximate 100(1 - α )% confidence interval for μ is ¯ x ± z α/ 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 - α )% CI for a population proportion p is ˆ p ± z α/ 2 q ˆ p ˆ q/n. 3. One-sided confidence interval: An upper confidence bound for μ is μ < ¯ x + z α s/ n and a lower confidence bound for μ is μ > ¯ x - z α s/ n. 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 ( X i = 1) = p . > X<-rbinom(100,1,0.4)
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  • Fall '04
  • Chung
  • Statistics, one-sided confidence interval, Moo K. Chung, stan¯ dard deviation

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