# 10_14_09ans - STAT 409 1. Examples for 10/14/2009 (Answers)...

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STAT 409 Examples for 10/14/2009 (Answers) Fall 2009 1. Claim: δ < 7 H 0 : δ 7 H 1 : δ < 7 Test Statistic: T = 8 4 7 5 D D 0 δ - = - n s = 1.4142. Rejection Region: Reject H 0 if T < – t 0.05 ( 8 – 1 = 7 d.f. ) = – 1.895. The value of the test statistic does not fall into the Rejection Region. Do NOT Reject H 0 at α = 0.05 . ( p-value 0.10. ) 2. 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: ( 29 ( 29 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 .

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3. Claim: σ < 1 H 0 : σ 1 vs. H 1 : σ < 1 s = 0.8. n = 25. Test Statistic:
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## This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.

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10_14_09ans - STAT 409 1. Examples for 10/14/2009 (Answers)...

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