# 12_02ans - STAT 410 Examples for Fall 2009 1 Let X 1 X 2 X...

This preview shows pages 1–2. Sign up to view the full content.

STAT 410 Examples for 12/02/2009 Fall 2009 1. Let X 1 , X 2 , … , X 16 be a random sample of size n = 16 from a N ( μ , σ 2 ) distribution. We are interested in testing H 0 : σ = 39 vs. H 1 : σ > 39. Recall: If X 1 , X 2 , … , X n are i.i.d. N ( μ , σ 2 ), then ( 29 2 2 σ S 1 n - is χ 2 ( n – 1 ). a) Find the “best” critical ( rejection ) region with the significance level α = 0.05. Test Statistic: ( 29 2 2 2 0 2 2 39 15 1 s σ s χ = = - n . Reject H 0 if 2 2 α χ χ ( n – 1 ) = 2 0.05 χ ( 15 ) = 25.00. 2 2 39 15 s > 25.00 s 2 > 2535 . b) Find the power of the test from part (a) at σ = 66.7. Power = P ( Reject H 0 | H 0 is not true ) = P ( S 2 > 2535 | σ = 66.7 ) = P ( ( 29 2 2 σ S 1 n - > 2 7 . 66 2535 15 | σ = 66.7 ) = P ( χ 2 ( 15 ) > 8.547 ) = 0.90 . c) What is the probability of Type II Error if σ = 66.7? P ( Type II Error ) = 1 – Power = 0.10 . The Chi-Square Distribution P ( X x ) 0.010 0.025 0.050 0.100 0.900 0.950 0.975 0.990 r ( 29 r 2 99 . 0 χ

This preview has intentionally blurred sections. Sign up to view the full version.

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

## This note was uploaded on 04/15/2010 for the course STAT 410 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

### Page1 / 4

12_02ans - STAT 410 Examples for Fall 2009 1 Let X 1 X 2 X...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online