EX 28 - STAT 400 Examples for 11/10/2011 (2) (Answers) Fall...

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STAT 400 Examples for 11/10/2011 (2) (Answers) Fall 2011 The χ 2 Distribution r χ 2 0.995 χ 2 0.99 χ 2 0.975 χ 2 0.95 χ 2 0.90 χ 2 0.10 χ 2 0.05 χ 2 0.025 χ 2 0.01 χ 2 0.005 24 9.886 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98 45.56 40 20.71 22.16 24.43 26.51 29.05 51.80 55.76 59.34 63.69 66.77 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 .
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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
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EX 28 - STAT 400 Examples for 11/10/2011 (2) (Answers) Fall...

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