# 10_12_11ans - STAT 409 Examples for(Answers n = 41 Fall...

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STAT 409 Examples for 10/12/2011 (Answers) Fall 2011 1. s = 0.02. n = 41. a) Claim: σ 2 0.0003 H 0 : σ 2 0.0003 vs. H 1 : σ 2 > 0.0003 s = 0.02. n = 41. Test Statistic: ( ) ( ) 0003 0 02 0 1 41 1 2 2 0 2 2 s . . n σ χ - = - = = 53.3333 . Rejection Region: Right – tailed. Reject H 0 if 2 2 α > χ χ n – 1 = 40 degrees of freedom. α = 0.05 2 05 0 . χ = 55.76 . Reject H 0 if 2 χ > 55.76. The value of the test statistic does not fall into the Rejection Region. Do NOT Reject H 0 at α = 0.05 . b) α = 0.10 2 10 0 . χ = 51.80 . Reject H 0 if 2 χ > 51.80. The value of the test statistic does fall into the Rejection Region. Reject H 0 at α = 0.10 . 2. Claim: σ < 0.5 H 0 : σ 0.5 vs. H 1 : σ < 0.5 s = 0.4. n = 25. Test Statistic: ( ) ( ) 2 2 2 0 2 2 5 . 0 4 . 0 1 25 1 σ s χ - = - = n = 15.36 .

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Rejection Region: Left – tailed. Reject H 0 if 2 1 2 α < - χ χ n – 1 = 24 degrees of freedom. α = 0.05 2 95 0 . χ = 13.85 . Reject
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## This note was uploaded on 10/13/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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10_12_11ans - STAT 409 Examples for(Answers n = 41 Fall...

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