lecture10 notes

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 312: Lecture 10 Confidence intervals for variance Moo K. Chung mchung@stat.wisc.edu August 13, 2004 1. Suppose the fat content of a hotdog follows normal distribution. 10 measurements are given. dchisq(y, 1) 0.25 dchisq(y, 5) 0 20 y 40 0.00 0.00 0 > 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 interval estimate of the unknown population variance. To solve this problem, we need to know the following fact. 0.15 20 y 40 dchisq(y, 10) dchisq(y, 20) 0 20 y 40 0.10 (n - 1)S 2 1 = 2 2 (Xj - X)2 2 n-1 j=1 0.00 n 0.00 0.06 0 2. Let X1 , , Xn be a random sample from N (, 2 ). 20 y 40 Quiz. What is the expectation of 2 ? n-1 > > > > > > y<- 0:50 par(mfrow=c(2,2)) plot(y,dchisq(y,1),type='l') plot(y,dchisq(y,5),type='l') plot(y,dchisq(y,10),type='l') plot(y,dchisq(y,20),type='l') 2 n distribution are defined as Figure 1: The density functions of 2 , 2 , 2 , 2 re1 5 10 20 spectively. Review problems. Example 7.15., Excercise 7.45. Exercise 7.47. Additional problem for lecture 09. > library(Devore6) > data(ex07.47) > attach(ex07.47) > ex07.47 strength 1 11.5 2 12.1 3 9.9 4 9.3 .... > a<-(strength>10) > a [1] TRUE TRUE FALSE FALSE... > length(a) [1] 48 > sum(a) [1] 13 3. Critical values for numbers that gives 2 2 P (2 1-/2,n < n < /2,n ) = 1 - 2 To find 2 0.975,9 and 0.025,9 that is need to con2 , we use R package: struct 95% CI for > qchisq(0.025,9) [1] 2.700389 > qchisq(0.975,9) [1] 19.02277 4. 100(1 - )% CI for 2 : (n - 1) 2 (n - 1) 2 s < 2 < 2 s 2 /2,n-1 1-/2,n-1 ...
View Full Document

This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at Wisconsin.

Ask a homework question - tutors are online