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

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Unformatted text preview: Stat 312: Lecture 09 Confidence intervals from normal population Moo K. Chung [email protected] September 30, 2004-1.5-1.0-0.5 0.0 0.5 1.0 1.5 16 18 20 22 24 26 28 30 Normal Q-Q Plot Theoretical Quantiles Sample Quantiles Figure 1: Normal probability plot showing normality of data. 1. Fat content of 10 randomly selected hotdogs is given by > x<-c(25.2,21.3,22.8,17.0,29.8, 21.0,25.5,16.0,20.9,19.5) We are interested in constructing a 95 % CI for the population mean fat content. Since the sample size is small, we can not apply large sample size results. Let us check the normality of data first using qqnorm(x) . So we can assume our data to follow a normal distribution but the variance is unknown. 2. If X i ∼ N ( μ,σ 2 ) , T ∼ ¯ X- μ S/ √ n ∼ t n- 1 , a t distribution with n- 1 degrees of freedom. As n → ∞ , t n → N (0 , 1) so for large sample size n , we can approximate t distribution with N (0 , 1) ....
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at University of Wisconsin.

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lecture09 notes - Stat 312 Lecture 09 Confidence intervals...

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